摘要
Based on the ideas in[9],an integer d<sup>0</sup>（v）,called the implicit degree of v whichsatisfies d<sup>0</sup>（v）≥d（v）,is associated with each vertex v of a graph G.It is proved that if theimplicit degree sequence d<sub>1</sub><sup>0</sup>,d<sub>2</sub><sup>0</sup>,…,d<sub>n</sub><sup>0</sup>（where d<sub>1</sub><sup>0</sup>≤d<sub>2</sub><sup>0</sup>≤…≤d<sub>n</sub><sup>0</sup>）of a simple graph G on n≥3vertices satisfiesd<sub>i</sub><sup>0</sup>≤i【n/2（?）d<sub>n-i</sub><sup>0</sup>≥n-i,then G is hamiltonian.This is an improvement of the well-known theorem of Chvatal（[4]）.
Based on the ideas in[9],an integer d^0(v),called the implicit degree of v whichsatisfies d^0(v)≥d(v),is associated with each vertex v of a graph G.It is proved that if theimplicit degree sequence d_1~0,d_2~0,…,d_n^0(where d_1~0≤d_2~0≤…≤d_n^0)of a simple graph G on n≥3vertices satisfies d_i^0≤i<n/2■d_(n-i)~0≥n-i,then G is hamiltonian.This is an improvement of the well-known theorem of Chvatal([4]).
