{"title":"ON INTERVAL EDGE-COLORINGS OF COMPLETE MULTIPARTITE GRAPHS","authors":"Levon N. Muradyan","doi":"10.46991/pysu:a/2022.56.1.019","DOIUrl":null,"url":null,"abstract":"A graph $G$ is called a complete $r$-partite $(r\\geq 2)$ graph, if its vertices can be divided into $r$ non-empty independent sets $V_1,\\ldots,V_r$ in a way that each vertex in $V_i$ is adjacent to all the other vertices in $V_j$ for $1\\leq i<j\\leq r$. Let $K_{n_{1},n_{2},\\ldots,n_{r}}$ denote a complete $r$-partite graph with independent sets $V_1,V_2,\\ldots,V_r$ of sizes $n_{1},n_{2},\\ldots,n_{r}$. An edge-coloring of a graph $G$ with colors $1,2,\\ldots,t$ is called an \\emph{interval $t$-coloring}, if all colors are used and the colors of edges incident to each vertex of $G$ are distinct and form an interval of integers. In this paper we have obtained some results on the existence and construction of interval edge-colorings of complete $r$-partite graphs. Moreover, we have also derived an upper bound on the number of colors in interval colorings of complete multipartite graphs.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the YSU A: Physical and Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46991/pysu:a/2022.56.1.019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A graph $G$ is called a complete $r$-partite $(r\geq 2)$ graph, if its vertices can be divided into $r$ non-empty independent sets $V_1,\ldots,V_r$ in a way that each vertex in $V_i$ is adjacent to all the other vertices in $V_j$ for $1\leq i
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