{"title":"关于一些完全三部图的色唯一性","authors":"P. A. Gein","doi":"10.15826/umj.2021.1.004","DOIUrl":null,"url":null,"abstract":"Let \\(P(G, x)\\) be a chromatic polynomial of a graph \\(G\\). Two graphs \\(G\\) and \\(H\\) are called chromatically equivalent iff \\(P(G, x) = H(G, x)\\). A graph \\(G\\) is called chromatically unique if \\(G\\simeq H\\) for every \\(H\\) chromatically equivalent to \\(G\\). In this paper, the chromatic uniqueness of complete tripartite graphs \\(K(n_1, n_2, n_3)\\) is proved for \\(n_1 \\geqslant n_2 \\geqslant n_3 \\geqslant 2\\) and \\(n_1 - n_3 \\leqslant 5\\).","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":"19 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"ON CHROMATIC UNIQUENESS OF SOME COMPLETE TRIPARTITE GRAPHS\",\"authors\":\"P. A. Gein\",\"doi\":\"10.15826/umj.2021.1.004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let \\\\(P(G, x)\\\\) be a chromatic polynomial of a graph \\\\(G\\\\). Two graphs \\\\(G\\\\) and \\\\(H\\\\) are called chromatically equivalent iff \\\\(P(G, x) = H(G, x)\\\\). A graph \\\\(G\\\\) is called chromatically unique if \\\\(G\\\\simeq H\\\\) for every \\\\(H\\\\) chromatically equivalent to \\\\(G\\\\). In this paper, the chromatic uniqueness of complete tripartite graphs \\\\(K(n_1, n_2, n_3)\\\\) is proved for \\\\(n_1 \\\\geqslant n_2 \\\\geqslant n_3 \\\\geqslant 2\\\\) and \\\\(n_1 - n_3 \\\\leqslant 5\\\\).\",\"PeriodicalId\":36805,\"journal\":{\"name\":\"Ural Mathematical Journal\",\"volume\":\"19 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ural Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15826/umj.2021.1.004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ural Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15826/umj.2021.1.004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
ON CHROMATIC UNIQUENESS OF SOME COMPLETE TRIPARTITE GRAPHS
Let \(P(G, x)\) be a chromatic polynomial of a graph \(G\). Two graphs \(G\) and \(H\) are called chromatically equivalent iff \(P(G, x) = H(G, x)\). A graph \(G\) is called chromatically unique if \(G\simeq H\) for every \(H\) chromatically equivalent to \(G\). In this paper, the chromatic uniqueness of complete tripartite graphs \(K(n_1, n_2, n_3)\) is proved for \(n_1 \geqslant n_2 \geqslant n_3 \geqslant 2\) and \(n_1 - n_3 \leqslant 5\).