{"title":"A solution to the 1-2-3 conjecture","authors":"Ralph Keusch","doi":"10.1016/j.jctb.2024.01.002","DOIUrl":null,"url":null,"abstract":"<div><p>We show that for every graph without isolated edge, the edges can be assigned weights from <span><math><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></span> so that no two neighbors receive the same sum of incident edge weights. This solves a conjecture of Karoński, Łuczak, and Thomason from 2004.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"166 ","pages":"Pages 183-202"},"PeriodicalIF":1.2000,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series B","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0095895624000030","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We show that for every graph without isolated edge, the edges can be assigned weights from so that no two neighbors receive the same sum of incident edge weights. This solves a conjecture of Karoński, Łuczak, and Thomason from 2004.
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.