A solution to the 1-2-3 conjecture

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2024-01-26 DOI:10.1016/j.jctb.2024.01.002

Ralph Keusch

引用次数: 0

Abstract

We show that for every graph without isolated edge, the edges can be assigned weights from ${1, 2, 3}$ so that no two neighbors receive the same sum of incident edge weights. This solves a conjecture of Karoński, Łuczak, and Thomason from 2004.

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1-2-3 猜想的解决方案

我们证明，对于每一个没有孤立边的图，都可以从 {1,2,3} 中分配边的权重，这样就不会有两个邻居获得相同的入射边权重总和。这解决了 Karoński、Łuczak 和 Thomason 在 2004 年提出的一个猜想。

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

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.