无爪图的支撑k-端点树的存在性  

Existence of spanning k-ended trees in claw-free graphs

作　　者：严政[1] 李丽珠 YAN Zheng;LI Lizhu(College of Information and Mathematics,Yangtze University,Jingzhou 434000,Hubei China)

机构地区：[1]长江大学信息与数学学院,湖北荆州434000

出　　处：《中南民族大学学报（自然科学版）》2024年第3期424-427,共4页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(12271061);湖北省教育厅科学技术研究资助项目(D20191303)。

摘　　要：树T中度为1的点称为叶子,叶子数目不超过k的树称为k-端点树.图中存在一个哈密尔顿路,说明图中存在恰好含有两个叶子的支撑树.自然就有了关于哈密尔顿路问题的一个推广:考虑图中至多有k个叶子的支撑树即支撑k-端点树的存在性问题.通过控制集参数,确定了连通无爪图中存在支撑k-端点树条件.Let T be a tree.A vertex of degree one is a leaf of T.A tree having at most k leaves is called a k-ended tree.A Hamiltonian path is a spanning tree having exactly two leaves.From this point of view,some sufficient conditions for a graph to have a Hamiltonian path are modified to those for a spanning k-ended tree.A sufficient condition using dominating set is given for a connected claw-free graph who has spanning k-ended tree.

关 键 词：无爪图 支撑树 叶子 控制集 

分 类 号：O157.5[理学—数学]