在没有周期长度为0模4的图上

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2025-08-20 DOI:10.1016/j.jctb.2025.07.008

Ervin Győri , Binlong Li , Nika Salia , Casey Tompkins , Kitti Varga , Manran Zhu

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引用次数: 0

摘要

Bollobás证明了对于每一个k和r，使得k z + r包含一个偶数，一个n顶点的图，不包含长度为r modk的循环，最多只能包含一个线性数的边。这种图中最大边数的精确（或渐近）值对于很少的对（r和k）是已知的。在这项工作中，我们精确地确定了不包含长度为0mod4的循环的图中的最大边数。

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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On graphs without cycles of length 0 modulo 4

Bollobás proved that for every k and ℓ such that

k Z + ℓ

contains an even number, an n-vertex graph containing no cycle of length

ℓ \mod k

can contain at most a linear number of edges. The precise (or asymptotic) value of the maximum number of edges in such a graph is known for very few pairs ℓ and k. In this work we precisely determine the maximum number of edges in a graph containing no cycle of length

0 \mod 4

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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.