{"title":"由态射生成的有向分裂图的半可及性","authors":"Kittitat Iamthong, S. Kitaev","doi":"10.4310/joc.2023.v14.n1.a5","DOIUrl":null,"url":null,"abstract":"A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\\rightarrow u_2\\rightarrow \\cdots \\rightarrow u_t$, $t \\geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\\rightarrow u_j$ exist for $1 \\leq i<j \\leq t$. In this paper, we study semi-transitivity of families of directed split graphs obtained by iterations of morphisms applied to the adjacency matrices and giving in the limit infinite directed split graphs. A split graph is a graph in which the vertices can be partitioned into a clique and an independent set. We fully classify semi-transitive infinite directed split graphs when a morphism in question can involve any $n\\times m$ matrices over $\\{-1,0,1\\}$ with a single natural condition.","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"15 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Semi-transitivity of directed split graphs generated by morphisms\",\"authors\":\"Kittitat Iamthong, S. Kitaev\",\"doi\":\"10.4310/joc.2023.v14.n1.a5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\\\\rightarrow u_2\\\\rightarrow \\\\cdots \\\\rightarrow u_t$, $t \\\\geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\\\\rightarrow u_j$ exist for $1 \\\\leq i<j \\\\leq t$. In this paper, we study semi-transitivity of families of directed split graphs obtained by iterations of morphisms applied to the adjacency matrices and giving in the limit infinite directed split graphs. A split graph is a graph in which the vertices can be partitioned into a clique and an independent set. We fully classify semi-transitive infinite directed split graphs when a morphism in question can involve any $n\\\\times m$ matrices over $\\\\{-1,0,1\\\\}$ with a single natural condition.\",\"PeriodicalId\":44683,\"journal\":{\"name\":\"Journal of Combinatorics\",\"volume\":\"15 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/joc.2023.v14.n1.a5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/joc.2023.v14.n1.a5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Semi-transitivity of directed split graphs generated by morphisms
A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\rightarrow u_2\rightarrow \cdots \rightarrow u_t$, $t \geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\rightarrow u_j$ exist for $1 \leq i
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