路因子临界覆盖图存在的若干充分条件
The Sufficient Conditions for the Existence of Path-Factor Critical Covered Graphs
袁园1
作者信息
- 1. 海南大学数学与统计学院,海南海口 570228
- 折叠
摘要
设G是一个图,如果G的支撑子图F的每个分支都是一条路,则称F是路因子.P≥t-因子表示每个分支至少含有t个顶点的路因子.对于任意e∈E(G),如果图G存在P≥t-因子包含边e,则称图G是P≥t-因子覆盖的.对于图G的任意顶点子集S,|S|=k,如果G-S是P≥t-因子覆盖的,则称G是P≥t-因子临界覆盖的.本文考虑P≥t-因子临界覆盖图存在的几个充分条件,且通过给出极图说明在某种意义下给出的界是最好的.
Abstract
Let G be a graph.A spanning subgraph F of G is called a path factor if each component of F is a path.Denote by P≥t-factor the path factor each component of which admits at least t vertices.We say that G is P≥t-factor covered if G has a P≥t-factor containing e for any e ∈ E(G).For arbitrary S⊆ V(G)with | S|=k,if C-S is P≥f-factor covered,then we say G is P≥t-factor-critical covered.In this paper,we present sufficient conditions for graphs to be P≥t-factor-critical covered and construct counterexamples to show that the bounds are best possible in some sense.
关键词
联结数/连通度/路因子/P≥t-因子/P≥t-因子临界覆盖图Key words
Binding number/connectivity/path factor/P≥t-factor/P≥t-factor-critical covered graph引用本文复制引用
基金项目
海南省自然科学基金青年基金(120QN176)
海南大学科研启动基金(KYQDZR19101)
出版年
2023
国家科技期刊平台
NSTL
万方数据