{"title":"H -线图的禁止子图刻画的不存在性","authors":"S. Varghese","doi":"10.37193/cmi.2023.01.11","DOIUrl":null,"url":null,"abstract":"$H$-line graph, denoted by $HL(G)$, is a generalization of line graph. Let $G$ and $H$ be two graphs such that $H$ has at least 3 vertices and is connected. The $H$-line graph of $G$, denoted by $HL(G)$, is that graph whose vertices are the edges of $G$ and two vertices of $HL(G)$ are adjacent if they are adjacent in $G$ and lie in a common copy of $H$. In this paper, we show that $H$-line graphs do not admit a forbidden subgraph characterization.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-existence of forbidden subgraph characterization of $H$-line graphs\",\"authors\":\"S. Varghese\",\"doi\":\"10.37193/cmi.2023.01.11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"$H$-line graph, denoted by $HL(G)$, is a generalization of line graph. Let $G$ and $H$ be two graphs such that $H$ has at least 3 vertices and is connected. The $H$-line graph of $G$, denoted by $HL(G)$, is that graph whose vertices are the edges of $G$ and two vertices of $HL(G)$ are adjacent if they are adjacent in $G$ and lie in a common copy of $H$. In this paper, we show that $H$-line graphs do not admit a forbidden subgraph characterization.\",\"PeriodicalId\":112946,\"journal\":{\"name\":\"Creative Mathematics and Informatics\",\"volume\":\"30 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Creative Mathematics and Informatics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37193/cmi.2023.01.11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Creative Mathematics and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37193/cmi.2023.01.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Non-existence of forbidden subgraph characterization of $H$-line graphs
$H$-line graph, denoted by $HL(G)$, is a generalization of line graph. Let $G$ and $H$ be two graphs such that $H$ has at least 3 vertices and is connected. The $H$-line graph of $G$, denoted by $HL(G)$, is that graph whose vertices are the edges of $G$ and two vertices of $HL(G)$ are adjacent if they are adjacent in $G$ and lie in a common copy of $H$. In this paper, we show that $H$-line graphs do not admit a forbidden subgraph characterization.
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