k-连通半无爪图的Hamilton性质

Hamiltonicity of k-connected Quasi-claw-free Graphs

半无爪图是包含无爪图的更大的图类。关于k-连通半无爪图,得到以下结果:G是k-连通的半无爪图(k≥2),如果对于G2的任意基数为k+1的独立集X,都有∑d(v)≥n-k,则G是Hamilton图。

The concept of quasi-claw-free graph is raised by Ainouche,and every claw-free graph is quasi-claw-free graph.The result is given ： A k-connected quasi-claw-free graph G,（k≥2） is Hamilton if ∑v∈X d（v）≥n-k holds for every independent set X of cardinality（k＋1） in G2.