{"title":"图与1-和","authors":"Jagdeep Singh","doi":"10.1007/s00373-023-02730-z","DOIUrl":null,"url":null,"abstract":"<p>A graph that can be generated from <span>\\(K_1\\)</span> using joins and 0-sums is called a cograph. We define a sesquicograph to be a graph that can be generated from <span>\\(K_1\\)</span> using joins, 0-sums, and 1-sums. We show that, like cographs, sesquicographs are closed under induced minors. Cographs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. We obtain an analogue of this result for sesquicographs, that is, we find those non-sesquicographs for which every proper induced subgraph is a sesquicograph.</p>","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Cographs and 1-Sums\",\"authors\":\"Jagdeep Singh\",\"doi\":\"10.1007/s00373-023-02730-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A graph that can be generated from <span>\\\\(K_1\\\\)</span> using joins and 0-sums is called a cograph. We define a sesquicograph to be a graph that can be generated from <span>\\\\(K_1\\\\)</span> using joins, 0-sums, and 1-sums. We show that, like cographs, sesquicographs are closed under induced minors. Cographs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. We obtain an analogue of this result for sesquicographs, that is, we find those non-sesquicographs for which every proper induced subgraph is a sesquicograph.</p>\",\"PeriodicalId\":12811,\"journal\":{\"name\":\"Graphs and Combinatorics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-12-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Graphs and Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00373-023-02730-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graphs and Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00373-023-02730-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
A graph that can be generated from \(K_1\) using joins and 0-sums is called a cograph. We define a sesquicograph to be a graph that can be generated from \(K_1\) using joins, 0-sums, and 1-sums. We show that, like cographs, sesquicographs are closed under induced minors. Cographs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. We obtain an analogue of this result for sesquicographs, that is, we find those non-sesquicographs for which every proper induced subgraph is a sesquicograph.
期刊介绍：
Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.
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