k-连通无爪图中的生成圈和控制圈

Hamilton Cycle and Dominating Cycle in k-Connected Claw-Free Graphs

用张存铨在文[2]中的方法!本文通过疏远边的度和给出k-连通无瓜图中存在汉密尔顿圈和控制圈的充分条件,作为文中定理的推论,证明了若对任意■∈E(G) d(k)+d(v)≥3n/k-6,则G有汉密尔顿圈;若对任意■∈E(G) d(k)+d(v)≥3n/(k+1)-3,则G有控制圈,这里G是k-连通无爪图。

By the method given by Cun-Quan Zhang in [2], we give sufficient conditions on the de- gree sum of remote edges for the existence of H-cycle and D-cycle in k-connected claw-free graphs. As Corollaries of our Theorems, we prove that if d(u)+d(v)≥3n/k-6 for every uv∈E(G), then G has a H-cycle, and if d(u)+d(v)≥3n/(k+1)-3 for every uv∈E(G), then G has a D-cycle, where G is a k-connected claw-free graph of order a.