A Strengthening on Consecutive Odd Cycles in Graphs of Given Minimum Degree

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-07-21 DOI:10.1002/jgt.23281

Hao Lin, Guanghui Wang, Wenling Zhou

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引用次数: 0

Abstract

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 $⌈ k / 2 ⌉$ 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 $k \in N$ . Moreover, we also improve some previous results about cycles of consecutive lengths.

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最小次给定图中连续奇环的一个强化

[J]。Combin。Ser的理论。B,[2018]推测每一个最小度数至少为k + 1的2连通非二部图都包含有K / 2个连续奇数长度的环。特别地，他们证明了当k是偶数时这个猜想成立。在本文中，我们对任意k∈N证实了这个猜想。此外，我们还改进了前人关于连续长度循环的一些结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .