A solution to the 1-2-3 conjecture

IF 1.2 1区 数学 Q1 MATHEMATICS
Ralph Keusch
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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.

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。
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来源期刊
CiteScore
2.70
自引率
14.30%
发文量
99
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.
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