Degree-balanced decompositions of cubic graphs

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2025-05-10 DOI:10.1016/j.ejc.2025.104169

Borut Lužar , Jakub Przybyło , Roman Soták

引用次数: 0

Abstract

We show that every cubic graph on

n

vertices contains a spanning subgraph in which the number of vertices of each degree deviates from

\frac{n}{4}

by at most

\frac{1}{2}

, up to three exceptions. This resolves the conjecture of Alon and Wei (2023) for cubic graphs.

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三次图的度平衡分解

我们证明了每个n个顶点的三次图都包含一个生成子图，其中每个度的顶点数与n4的偏差最多为12，最多有3个例外。这解决了Alon和Wei（2023）对三次图的猜想。

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

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.