完美整数k-匹配和k-因子临界图  

THE PERFECT INTEGER k-MATCHINGS AND k-FACTOR-CRITICAL GRAPHS

作　　者：张燕红 张磊 任海珍 ZHANG Yan-hong;ZHANG Lei;REN Hai-zhen(School of Mathematics and Statistics,Qinghai Normal University,Xining 810008,China;The State Key Laboratory of Tibetan Information Processing and Application,Xining 810008,China;Academy of Plateau,Science and Sustainability,Xining 810008,China)

机构地区：[1]青海师范大学数学与统计学院,西宁810008 [2]藏文信息处理与应用国家重点实验室,西宁810008 [3]高原科学与可持续发展研究院,西宁810008

出　　处：《数学杂志》2024年第3期189-194,共6页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(12161073);Natural Science Foundation of Qinghai province(2020-ZJ-924)。

摘　　要：本文研究完美整数k-匹配和k-因子临界图的存在性.扩张常数表示图的连通强度,对于正则图,利用扩张常数给出了完美整数k-匹配存在的一个充分条件,这推广了Hamers等人和Cioabǎ等人的结果.此外,对于正则图,基于扩张常数还给出了k-因子临界图存在的一个充分条件.This article investigates the existence of perfect integer k-matchings and k-factor critical graphs.The extension constant represents the connectivity strength of a graph.For regu-lar graphs,a suficient condition for the existence of perfect integer k-matching is given using the extension constant,which extends the results of Hamers et al.and Cioaba et al.In addition,for regular graphs,a suficient condition for the existence of k-factor-critical graphs based on extension constant is also given.

关 键 词：完美整数k-匹配 k-因子临界图 连通性 扩张常数 

分 类 号：O157.5[理学—数学] O153.1[理学—基础数学]