{"title":"步行支配和无 HHD 图形","authors":"Silvia B. Tondato","doi":"10.1007/s00373-024-02771-y","DOIUrl":null,"url":null,"abstract":"<p>HHD-free is the class of graphs which contain no house, hole, or domino as induced subgraph. It is known that HHD-free graphs can be characterized via LexBFS-ordering and via <span>\\(m^3\\)</span>-convexity. In this paper we present new characterizations of HHD-free via domination of paths and walks. To achieve this, in particular we concentrate our attention on <span>\\(m_3\\)</span> path, i.e, an induced path of length at least 3 between two non-adjacent vertices in a graph <i>G</i>. We show that the domination between induced paths, paths and walks versus <span>\\(m_3\\)</span> paths, gives rise to characterization of HHD-free. We also characterize the class of graphs in which every <span>\\(m_3\\)</span> path dominates every path, induced path, walk, and <span>\\(m_3\\)</span> path, respectively.</p>","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"92 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Walk Domination and HHD-Free Graphs\",\"authors\":\"Silvia B. Tondato\",\"doi\":\"10.1007/s00373-024-02771-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>HHD-free is the class of graphs which contain no house, hole, or domino as induced subgraph. It is known that HHD-free graphs can be characterized via LexBFS-ordering and via <span>\\\\(m^3\\\\)</span>-convexity. In this paper we present new characterizations of HHD-free via domination of paths and walks. To achieve this, in particular we concentrate our attention on <span>\\\\(m_3\\\\)</span> path, i.e, an induced path of length at least 3 between two non-adjacent vertices in a graph <i>G</i>. We show that the domination between induced paths, paths and walks versus <span>\\\\(m_3\\\\)</span> paths, gives rise to characterization of HHD-free. We also characterize the class of graphs in which every <span>\\\\(m_3\\\\)</span> path dominates every path, induced path, walk, and <span>\\\\(m_3\\\\)</span> path, respectively.</p>\",\"PeriodicalId\":12811,\"journal\":{\"name\":\"Graphs and Combinatorics\",\"volume\":\"92 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-05\",\"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/s00373-024-02771-y\",\"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/s00373-024-02771-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
HHD-free is the class of graphs which contain no house, hole, or domino as induced subgraph. It is known that HHD-free graphs can be characterized via LexBFS-ordering and via \(m^3\)-convexity. In this paper we present new characterizations of HHD-free via domination of paths and walks. To achieve this, in particular we concentrate our attention on \(m_3\) path, i.e, an induced path of length at least 3 between two non-adjacent vertices in a graph G. We show that the domination between induced paths, paths and walks versus \(m_3\) paths, gives rise to characterization of HHD-free. We also characterize the class of graphs in which every \(m_3\) path dominates every path, induced path, walk, and \(m_3\) path, respectively.
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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