摘要
The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G be a 2-connected claw-free graph of order n with minimum degreeδ(G)≥3.If for any three non-adjacent subgraphs H1,H2,H3 that are isomorphic to K1,K1,K2,respectively,there is d(H1)+d(H2)+d(H3)≥n+3,then for each pair of vertices u,v∈G that is not a cut set,there exists a Hamilton path between u and v.
The degree d（H） of a subgraph H of a graph G is ■, where N（u） denotes the neighbor set of the vertex u of G. In this paper, we prove the following result on the condition of the degrees of subgraphs. Let G be a 2-connected claw-free graph of order n with minimum degree δ（G）≥3. If for any three non-adjacent subgraphs H1, H2, H3 that are isomorphic to K1, K1, K2, respectively, there is d（H1） + d（H2） + d（H3）≥n + 3, then for each pair of vertices u, v∈G that is not a cut set, there exists a Hamilton path between u and v.
基金
supported by the National Natural Science Foundation of China(No.11871398)
the Natural Science Basic Research Plan in Shaanxi Province of China(Program No.2018JM1032)
the Fundamental Research Funds for the Central Universities(No.3102019ghjd003)
the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(No.ZZ2019031)
