To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successf...To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successful implementations of such heuristics, both the tasks of some modification of previously described graph invariants and the description of new invariants remain relevant. Many of the described invariants make it possible to distinguish a larger number of graphs in the real time of a computer program. In this paper, we propose an invariant for a special kind of directed graphs, namely, for tournaments. The last ones, from our point of view, are interesting because when fixing the order of vertices, the number of different tournaments is exactly equal to the number of undirected graphs, also with fixing the order of vertices. In the invariant we are considering, all possible tournaments consisting of a subset of vertices of a given digraph with the same set of arcs are iterated over. For such subset tournaments, the places are calculated in the usual way, which are summed up to obtain the final values of the points of the vertices;these points form the proposed invariant. As we expected, calculations of the new invariant showed that it does not coincide with the most natural invariant for tournaments, in which the number of points is calculated for each participant. So far, we have conducted a small number of computational experiments, and the minimum value of the pair correlation between the sequences representing these two invariants that we found is for dimension 15.展开更多
In this paper, we present a new sufficient condition on degrees for a bipartite tournament to be Hamiltonian, that is, if an n × n bipartite tournament T satisfies the condition W（n - 3）, then T is Hamiltonian,...In this paper, we present a new sufficient condition on degrees for a bipartite tournament to be Hamiltonian, that is, if an n × n bipartite tournament T satisfies the condition W（n - 3）, then T is Hamiltonian, except for four exceptional graphs. This result is shown to be best possible in a sense.展开更多
Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtour...Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtournament. Let t ( m, n, k, l ) = max{t( Tm,n，k, l ) : Tm,n∈Γm，n^*}, where t ( Tm,n, k, l ) is the number of k × l(k≥2,l≥2) transitive bipartite subtournaments contained in Tm,n∈Γm，n^*. We obtain a method of graph theory for solving some integral programmings, investigate the upper bounds of a(m,n) and obtain t (m,n, k，l).展开更多
Let T=(V,A)be a tournament of order n and T_i,…,T_m be diconnectedcomponents in T.If uv ∈A and P is a directed path of length k-1(k≥3)from u to v,We call P ∪{uv}a 1-antidirected cycle of length k.Let k be an integ...Let T=(V,A)be a tournament of order n and T_i,…,T_m be diconnectedcomponents in T.If uv ∈A and P is a directed path of length k-1(k≥3)from u to v,We call P ∪{uv}a 1-antidirected cycle of length k.Let k be an integer satisfying 3≤k≤n.If every arc e∈A is contained in a 1-antidirected cycle of length k,we will refer toT as arc k 1-antidirected cyclic.If T is arc k 1-antidirected cyclic for k=3,4,…,n,T iscalled arc 1-antidirected pancyclic.In this paper,we prove that T is arc 1-antidirectedpancyclic if and only if T satisfies one of the following conditions:(i)2≤m≤3 and forany T_i,every arc e∈T_i is contained in a Hamilton path in T_i;(ii)m=1,except some spe-cial tournaments which are to be shown.展开更多
The exploitation and utilization of the tour resources of tournament athletics, including skiling, boat sailing, archery, ice engraving, snow engrav ing, has become a new trend of the development of Chinese tourism. D...The exploitation and utilization of the tour resources of tournament athletics, including skiling, boat sailing, archery, ice engraving, snow engrav ing, has become a new trend of the development of Chinese tourism. Due to the un ique cold climate and superior geographic location,Harbin is a promising city f or developing tour resources of tournament athletics. Based on the analysis of t he superiority and peculiarity of Harbin,the speculation on development of tour resources of tournament athletics in Harbin is proposed as follows:1) Harbin s hould develop its special tour resources of tournament athletics associated with needs of market; 2) Harbin should take the advantages of rich resources and dev elop ice and snow entertainment in winter and travel for sight-seeing and spend ing summer; 3) the adjustment of the layout of ice and snow resources should be based on the idea of taking Harbin as the center and all-side opening at the la rge scale in the way of radiation; 4) tourism should be developed by the combine d efforts of various departments to make feasible plan, and the organizers shoul d pay much attention to ensuring the safety of tourists.展开更多
A framework is provided for analyzing the time and resource requirements for a tournament where matches are played to a best-of-N format, to ensure maximal use of available facilities and a maximal number of competito...A framework is provided for analyzing the time and resource requirements for a tournament where matches are played to a best-of-N format, to ensure maximal use of available facilities and a maximal number of competitors. A baseline of average length of games and number of games played per match is necessary. The analysis informing development of the framework was carried out in the context of the sport of golf croquet. Based on the results of this analysis, golf croquet tournaments should have four best-of-three matches scheduled per court per day to optimize playing time and minimize the need to play matches outside regular playing hours.展开更多
The Sports Garbage Pickup Tournament is a sports event that incorporates elements of competition into cleaning activities,as opposed to traditional cleaning activities.As of the end of December 2016,a total of 552 Spo...The Sports Garbage Pickup Tournament is a sports event that incorporates elements of competition into cleaning activities,as opposed to traditional cleaning activities.As of the end of December 2016,a total of 552 Sports Garbage Pickup Tournaments have been held,mobilizing a cumulative total number of 62,989 people.As each tournament brings a revenue of over 300,000 yen,the total sales so far would be more than 165,000,000 yen.This game was recently reported on the International Olympic Committee channel.The garbage issue,a social problem for local communities,should be solved by residents,visitors,and workers themselves through sports,cooperating with local governments.This is an eco-friendly sport aimed at“solving local social problems through sports.”Sports Garbage Pickup Tournaments can be held anywhere,inside the city or in a natural environment.In addition,the competition allows participants to visually understand the environmental capacity of garbage produced in the community,as the points are weighted according to the types of garbage.The Sports Garbage Pickup Tournament is an educational program for sustainable development with emphasis on experience,pursuit,and practice,and also an action-based program aimed at promoting spontaneous action.This is an optimal competition for participants to acquire skills through mutual communication.As children,adults,and people with disabilities can play together,the competition will promote communication across the generations.展开更多
Scheduling sports leagues has drawn significant attention to itself in recent years, as it involves considerable revenue as well as challenging combinatorial optimization problems. A particular class of these problems...Scheduling sports leagues has drawn significant attention to itself in recent years, as it involves considerable revenue as well as challenging combinatorial optimization problems. A particular class of these problems is the Traveling Tournament Problem (TTP) which focuses on minimizing the total traveling distance for teams. In this paper, an efficient simulated annealing approach is presented for TTP which applies two simultaneous and disparate models for the problem in order to search the solutions space more effectively. Also, a computationally efficient modified greedy scheme is proposed for constructing a favorable initial solution for the simulated annealing algorithm. Our computational experiments, carried out on standard instances, demonstrate that this approach competes with previous offered methods in quality of found solutions and their computational time.展开更多
The most important goal in civics education is to ensure that each citizen has a good understanding of ethics and moral behavior, and thus stresses the constant link between knowledge and practice. In this context, to...The most important goal in civics education is to ensure that each citizen has a good understanding of ethics and moral behavior, and thus stresses the constant link between knowledge and practice. In this context, to increase understanding of civics education for being able to create the best generation and condition in the future life, study on this issue is becoming a very crucial manner. In general, methods like discussion and dialogue are used to allow students to express themselves. However, cooperative learning in particular addresses many of the needs and concerns facing by educational systems and Team Game Tournament （TGT） method is one of the preferable methods of cooperative learning. This study was aiming to increase civics learning achievements by using cooperative learning based on TGT method on secondary school students of Jatisari of Indonesia. The action research procedure was also used so as to be able to evaluate the influent, impact, and result of TGT. Accordingly, cooperative learning with TGT method has successfully given positive contribution to increasing student learning civics achievement.展开更多
It is proved that for given integer k≥2, almost all k-hypertournaments are strong and in almost all k-hypertournaments, every pair of vertices lies on a 3-cycle.
Gutin and Rafiey（Australas J. Combin. 34（2006）, 17-21） provided an example of an n-partite tournament with exactly n-m ＋ 1 cycles of length of m for any given m with 4 ≤ m ≤ n, and posed the following question....Gutin and Rafiey（Australas J. Combin. 34（2006）, 17-21） provided an example of an n-partite tournament with exactly n-m ＋ 1 cycles of length of m for any given m with 4 ≤ m ≤ n, and posed the following question. Let 3 ≤ m ≤n and n ≥ 4. Are there strong n-partite tournaments, which are not themselves tournaments, with exactly n-m ＋ 1 cycles of length m for two values of m？ In the same paper,they showed that this question has a negative answer for two values n-1 and n. In this paper, we prove that a strong n-partite tournament with exactly two cycles of length n-1 must contain some given multipartite tournament as subdigraph. As a corollary, we also show that the above question has a negative answer for two values n-1 and any l with 3 ≤ l ≤ n and l ≠n-1.展开更多
Purpose This study examined the effects of tournament load on neuromuscular function,perceived wellness and coach rat-ings of performance across two 6-day netball tournaments.Methods Thirty-nine female youth netballer...Purpose This study examined the effects of tournament load on neuromuscular function,perceived wellness and coach rat-ings of performance across two 6-day netball tournaments.Methods Thirty-nine female youth netballers(age=14.6±0.5 years,stature=165.9±4.7 cm,body mass=56.5±7.2 kg)were categorised as HIGH(10-11 matches,n=20)or LOW(6 matches,n=19)tournament load.Match load,jump height,perceived wellness and coach ratings of performance were monitored daily.Results HIGH tournament load resulted in greater reductions in jump height on match-day 4(-8.3%,±5.6%)when compared to LOW.HIGH tournament load resulted in greater reductions in perceived soreness(-0.9,±1.1 AU)and overall wellness(-2.6,±2.3 AU)on match-day 3,and a greater reduction in perceived sleep(-0.9,±1.1 AU)on match-day 4.HIGH tournament load was negatively associated with sleep quality and coach ratings of performance(effect size correlation=-0.34 to-0.47)when compared to LOW.Conclusion Our results indicate that a higher tournament load resulted in greater increases in neuromuscular fatigue,reduced perceived wellness,and lower ratings of performance.Practitioners should consider pre-tournament preparation and monitoring strategies to minimise the physiological disturbances during an intensified tournament.展开更多
To explain China＇s dramatic economic growth, researchers have proposed a ＂tournament thesis. ＂＂ According to this thesis, the central government＇s ability to set growth targets has played a crucial role in growth...To explain China＇s dramatic economic growth, researchers have proposed a ＂tournament thesis. ＂＂ According to this thesis, the central government＇s ability to set growth targets has played a crucial role in growth since political promotion is largely based on local economic growth. We use provincial officials＂ career mobility data to test this thesis. For both time periods （1979-1995 and 1979-2002）, economic performance, measured in annual, average and relative terms, did not affect these officials＇ career advancement. We then sketch an alternative analytical framework to explain Chinese local officials＇ strong urge for developmentalism and, finally, draw policy implications from this explanatory framework.展开更多
In 1978, K. B. Reid proposed a conjecture as follows: 'Every finite and nonempty set S of positive integers is a set of scores for some tournaments'. And he proved that the conjecture is true for |S|=1, 2, 3. ...In 1978, K. B. Reid proposed a conjecture as follows: 'Every finite and nonempty set S of positive integers is a set of scores for some tournaments'. And he proved that the conjecture is true for |S|=1, 2, 3. In 1984, M. Hager展开更多
A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in ...A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V\{x} for some point x, and (2) every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.展开更多
The problem of complementary cycles in tournaments and bipartite tournaments was completely solved. However, the problem of complementary cycles in semicomplete n-partite digraphs with n 〉 3 is still open. Based on t...The problem of complementary cycles in tournaments and bipartite tournaments was completely solved. However, the problem of complementary cycles in semicomplete n-partite digraphs with n 〉 3 is still open. Based on the definition of componentwise complementary cycles, we get the following result. Let D be a 2-strong n-partite （n 〉 6） tournament that is not a tournament. Let C be a 3-cycle of D and D ／ V（C） be nonstrong. For the unique acyclic sequence D1, D2,..., Da of D ／ V（C）, where a 〉 2, let Dc = {Di｜Di contains cycles, i = 1,2,...,a}, Dc = {D1,D2,...,Da} ／ De. If Dc≠ 0, then D contains a pair of componentwise complementary cycles.展开更多
In this paper we prove that if T is a regular n-partite tournament with n ≥ 4, then each arc of T lies on a cycle whose vertices are from exactly k partite sets for k = 4, 5, . . . ,n. Our result, in a sense, general...In this paper we prove that if T is a regular n-partite tournament with n ≥ 4, then each arc of T lies on a cycle whose vertices are from exactly k partite sets for k = 4, 5, . . . ,n. Our result, in a sense, generalizes a theorem due to Alspach.展开更多
A tournament is an orientation of the complete graph.Tournaments form perhaps the most interesting class of digraphs and it has a great potential for application.Tournaments provide a model of the statistical techniqu...A tournament is an orientation of the complete graph.Tournaments form perhaps the most interesting class of digraphs and it has a great potential for application.Tournaments provide a model of the statistical technique called the method of paired comparisons and they have also been studied in connection with sociometric relations in small groups.In this paper,we investigate disjoint cycles of the same length in tournaments.In 2010,Lichiardopol conjectured that for given integers l≥3 and k≥1,any tournament with minimum out-degree at least(l-1)k-1 contains k disjoint l-cycles,where an l-cycle is a cycle of order l.Bang-Jensen et al.verified the conjecture for l=3 and Ma et al.proved that it also holds for l≥10.This paper provides a proof of the conjecture for the case of 9≥l≥4.展开更多
文摘To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successful implementations of such heuristics, both the tasks of some modification of previously described graph invariants and the description of new invariants remain relevant. Many of the described invariants make it possible to distinguish a larger number of graphs in the real time of a computer program. In this paper, we propose an invariant for a special kind of directed graphs, namely, for tournaments. The last ones, from our point of view, are interesting because when fixing the order of vertices, the number of different tournaments is exactly equal to the number of undirected graphs, also with fixing the order of vertices. In the invariant we are considering, all possible tournaments consisting of a subset of vertices of a given digraph with the same set of arcs are iterated over. For such subset tournaments, the places are calculated in the usual way, which are summed up to obtain the final values of the points of the vertices;these points form the proposed invariant. As we expected, calculations of the new invariant showed that it does not coincide with the most natural invariant for tournaments, in which the number of points is calculated for each participant. So far, we have conducted a small number of computational experiments, and the minimum value of the pair correlation between the sequences representing these two invariants that we found is for dimension 15.
文摘In this paper, we present a new sufficient condition on degrees for a bipartite tournament to be Hamiltonian, that is, if an n × n bipartite tournament T satisfies the condition W（n - 3）, then T is Hamiltonian, except for four exceptional graphs. This result is shown to be best possible in a sense.
文摘Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtournament. Let t ( m, n, k, l ) = max{t( Tm,n，k, l ) : Tm,n∈Γm，n^*}, where t ( Tm,n, k, l ) is the number of k × l(k≥2,l≥2) transitive bipartite subtournaments contained in Tm,n∈Γm，n^*. We obtain a method of graph theory for solving some integral programmings, investigate the upper bounds of a(m,n) and obtain t (m,n, k，l).
文摘Let T=(V,A)be a tournament of order n and T_i,…,T_m be diconnectedcomponents in T.If uv ∈A and P is a directed path of length k-1(k≥3)from u to v,We call P ∪{uv}a 1-antidirected cycle of length k.Let k be an integer satisfying 3≤k≤n.If every arc e∈A is contained in a 1-antidirected cycle of length k,we will refer toT as arc k 1-antidirected cyclic.If T is arc k 1-antidirected cyclic for k=3,4,…,n,T iscalled arc 1-antidirected pancyclic.In this paper,we prove that T is arc 1-antidirectedpancyclic if and only if T satisfies one of the following conditions:(i)2≤m≤3 and forany T_i,every arc e∈T_i is contained in a Hamilton path in T_i;(ii)m=1,except some spe-cial tournaments which are to be shown.
文摘The exploitation and utilization of the tour resources of tournament athletics, including skiling, boat sailing, archery, ice engraving, snow engrav ing, has become a new trend of the development of Chinese tourism. Due to the un ique cold climate and superior geographic location,Harbin is a promising city f or developing tour resources of tournament athletics. Based on the analysis of t he superiority and peculiarity of Harbin,the speculation on development of tour resources of tournament athletics in Harbin is proposed as follows:1) Harbin s hould develop its special tour resources of tournament athletics associated with needs of market; 2) Harbin should take the advantages of rich resources and dev elop ice and snow entertainment in winter and travel for sight-seeing and spend ing summer; 3) the adjustment of the layout of ice and snow resources should be based on the idea of taking Harbin as the center and all-side opening at the la rge scale in the way of radiation; 4) tourism should be developed by the combine d efforts of various departments to make feasible plan, and the organizers shoul d pay much attention to ensuring the safety of tourists.
文摘A framework is provided for analyzing the time and resource requirements for a tournament where matches are played to a best-of-N format, to ensure maximal use of available facilities and a maximal number of competitors. A baseline of average length of games and number of games played per match is necessary. The analysis informing development of the framework was carried out in the context of the sport of golf croquet. Based on the results of this analysis, golf croquet tournaments should have four best-of-three matches scheduled per court per day to optimize playing time and minimize the need to play matches outside regular playing hours.
文摘The Sports Garbage Pickup Tournament is a sports event that incorporates elements of competition into cleaning activities,as opposed to traditional cleaning activities.As of the end of December 2016,a total of 552 Sports Garbage Pickup Tournaments have been held,mobilizing a cumulative total number of 62,989 people.As each tournament brings a revenue of over 300,000 yen,the total sales so far would be more than 165,000,000 yen.This game was recently reported on the International Olympic Committee channel.The garbage issue,a social problem for local communities,should be solved by residents,visitors,and workers themselves through sports,cooperating with local governments.This is an eco-friendly sport aimed at“solving local social problems through sports.”Sports Garbage Pickup Tournaments can be held anywhere,inside the city or in a natural environment.In addition,the competition allows participants to visually understand the environmental capacity of garbage produced in the community,as the points are weighted according to the types of garbage.The Sports Garbage Pickup Tournament is an educational program for sustainable development with emphasis on experience,pursuit,and practice,and also an action-based program aimed at promoting spontaneous action.This is an optimal competition for participants to acquire skills through mutual communication.As children,adults,and people with disabilities can play together,the competition will promote communication across the generations.
文摘Scheduling sports leagues has drawn significant attention to itself in recent years, as it involves considerable revenue as well as challenging combinatorial optimization problems. A particular class of these problems is the Traveling Tournament Problem (TTP) which focuses on minimizing the total traveling distance for teams. In this paper, an efficient simulated annealing approach is presented for TTP which applies two simultaneous and disparate models for the problem in order to search the solutions space more effectively. Also, a computationally efficient modified greedy scheme is proposed for constructing a favorable initial solution for the simulated annealing algorithm. Our computational experiments, carried out on standard instances, demonstrate that this approach competes with previous offered methods in quality of found solutions and their computational time.
文摘The most important goal in civics education is to ensure that each citizen has a good understanding of ethics and moral behavior, and thus stresses the constant link between knowledge and practice. In this context, to increase understanding of civics education for being able to create the best generation and condition in the future life, study on this issue is becoming a very crucial manner. In general, methods like discussion and dialogue are used to allow students to express themselves. However, cooperative learning in particular addresses many of the needs and concerns facing by educational systems and Team Game Tournament （TGT） method is one of the preferable methods of cooperative learning. This study was aiming to increase civics learning achievements by using cooperative learning based on TGT method on secondary school students of Jatisari of Indonesia. The action research procedure was also used so as to be able to evaluate the influent, impact, and result of TGT. Accordingly, cooperative learning with TGT method has successfully given positive contribution to increasing student learning civics achievement.
文摘It is proved that for given integer k≥2, almost all k-hypertournaments are strong and in almost all k-hypertournaments, every pair of vertices lies on a 3-cycle.
基金supported by the Natural Science Young Foundation of China(No.11701349)by the Natural Science Foundation of Shanxi Province,China(No.201601D011005)by Shanxi Scholarship Council of China(2017-018)
文摘Gutin and Rafiey（Australas J. Combin. 34（2006）, 17-21） provided an example of an n-partite tournament with exactly n-m ＋ 1 cycles of length of m for any given m with 4 ≤ m ≤ n, and posed the following question. Let 3 ≤ m ≤n and n ≥ 4. Are there strong n-partite tournaments, which are not themselves tournaments, with exactly n-m ＋ 1 cycles of length m for two values of m？ In the same paper,they showed that this question has a negative answer for two values n-1 and n. In this paper, we prove that a strong n-partite tournament with exactly two cycles of length n-1 must contain some given multipartite tournament as subdigraph. As a corollary, we also show that the above question has a negative answer for two values n-1 and any l with 3 ≤ l ≤ n and l ≠n-1.
文摘Purpose This study examined the effects of tournament load on neuromuscular function,perceived wellness and coach rat-ings of performance across two 6-day netball tournaments.Methods Thirty-nine female youth netballers(age=14.6±0.5 years,stature=165.9±4.7 cm,body mass=56.5±7.2 kg)were categorised as HIGH(10-11 matches,n=20)or LOW(6 matches,n=19)tournament load.Match load,jump height,perceived wellness and coach ratings of performance were monitored daily.Results HIGH tournament load resulted in greater reductions in jump height on match-day 4(-8.3%,±5.6%)when compared to LOW.HIGH tournament load resulted in greater reductions in perceived soreness(-0.9,±1.1 AU)and overall wellness(-2.6,±2.3 AU)on match-day 3,and a greater reduction in perceived sleep(-0.9,±1.1 AU)on match-day 4.HIGH tournament load was negatively associated with sleep quality and coach ratings of performance(effect size correlation=-0.34 to-0.47)when compared to LOW.Conclusion Our results indicate that a higher tournament load resulted in greater increases in neuromuscular fatigue,reduced perceived wellness,and lower ratings of performance.Practitioners should consider pre-tournament preparation and monitoring strategies to minimise the physiological disturbances during an intensified tournament.
基金financial support from the China National Social Science Foundation key project(11-ZD037)the British SPF fund+1 种基金the Fundamental Research Funds for the Central Universities the Research Funds of Renmin University of China over our fieldwork in the past several years
文摘To explain China＇s dramatic economic growth, researchers have proposed a ＂tournament thesis. ＂＂ According to this thesis, the central government＇s ability to set growth targets has played a crucial role in growth since political promotion is largely based on local economic growth. We use provincial officials＂ career mobility data to test this thesis. For both time periods （1979-1995 and 1979-2002）, economic performance, measured in annual, average and relative terms, did not affect these officials＇ career advancement. We then sketch an alternative analytical framework to explain Chinese local officials＇ strong urge for developmentalism and, finally, draw policy implications from this explanatory framework.
文摘In 1978, K. B. Reid proposed a conjecture as follows: 'Every finite and nonempty set S of positive integers is a set of scores for some tournaments'. And he proved that the conjecture is true for |S|=1, 2, 3. In 1984, M. Hager
基金supported by National Natural Science Foundation of China (Grant Nos.10771051,10831002)
文摘A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V\{x} for some point x, and (2) every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.
基金Supported by the National Natural Science Foundation of China (No. 10801114)the Nature Science Foundation of Shandong Province, China (No. ZR2011AL019 No. ZR2011AM005)
文摘The problem of complementary cycles in tournaments and bipartite tournaments was completely solved. However, the problem of complementary cycles in semicomplete n-partite digraphs with n 〉 3 is still open. Based on the definition of componentwise complementary cycles, we get the following result. Let D be a 2-strong n-partite （n 〉 6） tournament that is not a tournament. Let C be a 3-cycle of D and D ／ V（C） be nonstrong. For the unique acyclic sequence D1, D2,..., Da of D ／ V（C）, where a 〉 2, let Dc = {Di｜Di contains cycles, i = 1,2,...,a}, Dc = {D1,D2,...,Da} ／ De. If Dc≠ 0, then D contains a pair of componentwise complementary cycles.
基金supported by Chinese Postdoctoral Science FoundationNational Natural Science Foundation of China(Grant Nos.60103021,10171062 and 19871040)Huazhong University of Science and Technology Foundation
文摘In this paper we prove that if T is a regular n-partite tournament with n ≥ 4, then each arc of T lies on a cycle whose vertices are from exactly k partite sets for k = 4, 5, . . . ,n. Our result, in a sense, generalizes a theorem due to Alspach.
基金supported by the National Natural Science Foundation of China(Nos.12071260,11671232)。
文摘A tournament is an orientation of the complete graph.Tournaments form perhaps the most interesting class of digraphs and it has a great potential for application.Tournaments provide a model of the statistical technique called the method of paired comparisons and they have also been studied in connection with sociometric relations in small groups.In this paper,we investigate disjoint cycles of the same length in tournaments.In 2010,Lichiardopol conjectured that for given integers l≥3 and k≥1,any tournament with minimum out-degree at least(l-1)k-1 contains k disjoint l-cycles,where an l-cycle is a cycle of order l.Bang-Jensen et al.verified the conjecture for l=3 and Ma et al.proved that it also holds for l≥10.This paper provides a proof of the conjecture for the case of 9≥l≥4.
