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

作　　者：袁园 Yuan Yuan(School of Mathematics and Statistics,Hainan University,Haikou 570228,China)

机构地区：[1]海南大学数学与统计学院,海南海口570228

出　　处：《南京师大学报（自然科学版）》2023年第4期11-16,共6页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：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).

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.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 SV(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.

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 

分 类 号：O5[理学—物理] C70[社会学] O5C38