{K_(1,4),K_(1,4)+e}-free图Hamilton性的邻集交条件

Neighborhood intersection condition of Hamiltonian property in{K_(1,4),K_(1,4)+e}-free graph

设G是阶为n(n≥3)的2一连通{K_(1,4),K_(1,4)+e}-free图,连通度为k,给出了{K_(1,4),K_(1,4)+e}图的Hamilton性的邻集交条件,即如果对于每一个k+1个点的独立集S,存在u,v∈S,有|N(u)∩N(v)|≥max{n-k-2/4,2},则G是Hamilton图.

Let G be a 2-connected{K_(1,4),K_(1,4)+e}-free graph of order n(n≥3)and connectivityk,the neighborhood intersection condition of Hamiltonian property in{K_(1,4),K_(1,4)+e}-free graph was given,that is,if for any independent setSof cardinality k+1,there exist u,v∈S,implies|N(u)∩N(v)|≥max{n-k-2/4,2},then G is a Hamilton graph.