For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain th...For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain that if G is a 2-connected graph on n vertices such that the implicit degree sum of any three independent vertices is at least n ＋ 1, then either G contains a hamiltonian path, or c（G） 〉 p（G） - 1.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11501322)the Postdoctoral Science Foundation of China(Grant No.2015M571999)the Natural Science Foundation of Shandong Province(Grant No.ZR2014AP002)
文摘For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain that if G is a 2-connected graph on n vertices such that the implicit degree sum of any three independent vertices is at least n ＋ 1, then either G contains a hamiltonian path, or c（G） 〉 p（G） - 1.
