The Distance Matching Extension in K1,k-free Graphs with High Local Connectedness

• 作者: Wei-chan LIU Gui-ying YAN
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 37-43
• 页数: 7页
• 语种: 英文

摘要

A matching is extendable in a graph G if G has a perfect matching containing it.A distance q matching is a matching such that the distance between any two distinct matching edges is at least q.In this paper,we prove that any distance 2k-3 matching is extendable in a connected and locally(k-1)-connected K1,k-free graph of even order.Furthermore,we also prove that any distance q matching M in an r-connected and locally(k-1)-connected K1,k-free graph of even order is extendable provided that |M| is bounded by a function on r,k and q.Our results improve some results in[J.Graph Theory 93(2020),5-20].