A strengthening on consecutive odd cycles in graphs of given minimum degree

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Lin, Hao, Wang, Guanghui, Zhou, Wenling
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913915717287936
author Lin, Hao
Wang, Guanghui
Zhou, Wenling
author_facet Lin, Hao
Wang, Guanghui
Zhou, Wenling
contents Liu and Ma [J. Combin. Theory Ser. B, 2018] conjectured that every $2$-connected non-bipartite graph with minimum degree at least $k+1$ contains $\lceil k/2\rceil $ cycles with consecutive odd lengths. In particular, they showed that this conjecture holds when $k$ is even. In this paper, we confirm this conjecture for any $k\in \mathbb N$. Moreover, we also improve some previous results about cycles of consecutive lengths.
format Preprint
id arxiv_https___arxiv_org_abs_2410_00648
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A strengthening on consecutive odd cycles in graphs of given minimum degree
Lin, Hao
Wang, Guanghui
Zhou, Wenling
Combinatorics
Liu and Ma [J. Combin. Theory Ser. B, 2018] conjectured that every $2$-connected non-bipartite graph with minimum degree at least $k+1$ contains $\lceil k/2\rceil $ cycles with consecutive odd lengths. In particular, they showed that this conjecture holds when $k$ is even. In this paper, we confirm this conjecture for any $k\in \mathbb N$. Moreover, we also improve some previous results about cycles of consecutive lengths.
title A strengthening on consecutive odd cycles in graphs of given minimum degree
topic Combinatorics
url https://arxiv.org/abs/2410.00648