[1]袁 园.路因子临界覆盖图存在的若干充分条件[J].南京师大学报(自然科学版),2023,46(04):11-16.[doi:10.3969/j.issn.1001-4616.2023.04.003]
　Yuan Yuan.The Sufficient Conditions for the Existence of Path-Factor Critical Covered Graphs[J].Journal of Nanjing Normal University(Natural Science Edition),2023,46(04):11-16.[doi:10.3969/j.issn.1001-4616.2023.04.003]
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路因子临界覆盖图存在的若干充分条件()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第46卷
期数:
2023年04期
页码:
11-16
栏目:
数学
出版日期:
2023-12-15

文章信息/Info

Title:
The Sufficient Conditions for the Existence of Path-Factor Critical Covered Graphs
文章编号:
1001-4616(2023)04-0011-06
作者:
袁 园
(海南大学数学与统计学院,海南 海口 570228)
Author(s):
Yuan Yuan
(School of Mathematics and Statistics,Hainan University,Haikou 570228,China)
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
Keywords:
Binding number;  connectivity;  path factor;  P≥t-factor;  P≥t-factor-critical covered graph
分类号:
05C70; 05C38
DOI:
10.3969/j.issn.1001-4616.2023.04.003
文献标志码:
A
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 G-S is P≥t-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.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2023-04-06.
基金项目:海南省自然科学基金青年基金项目(120QN176)、海南大学科研启动基金项目(KYQD(ZR)19101).
通讯作者:袁园,博士,讲师,研究方向:图论. E-mail:kuailenanshi@126.com
更新日期/Last Update: 2023-12-15