Minimum degree stability of C2k+1 ${C}_{2k+1}$‐free graphs-Reference-Cited by-同舟云学术

Minimum degree stability of C2k+1 ${C}_{2k+1}$‐free graphs

Published:2024-02-11 Issue:2 Volume:106 Page:307-321
ISSN:0364-9024
Container-title:Journal of Graph Theory
language:en
Short-container-title:Journal of Graph Theory

Author:

Yuan Xiaoli¹,Peng Yuejian¹^ORCID

Affiliation:

1. School of Mathematics Hunan University Changsha China

Abstract

AbstractWe consider the minimum degree stability of graphs forbidding odd cycles: What is the tight bound on the minimum degree to guarantee that the structure of a ‐free graph inherits from the extremal graph (a balanced complete bipartite graph)? Andrásfai, Erdős, and Sós showed that if a ‐free graph on vertices has minimum degree greater than , then it is bipartite. Häggkvist showed that for , if a ‐free graph on vertices has minimum degree greater than , then it is bipartite. Häggkvist also pointed out that this result cannot be extended to . In this paper, we give a complete answer for any . We show that if and is an ‐vertex ‐free graph with , then is bipartite, and the bound is tight.

Funder

National Natural Science Foundation of China

Publisher

Wiley

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/jgt.23086

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