{"title":"Vertex decomposability of complexes associated to forests","authors":"Anurag Singh","doi":"10.22108/TOC.2021.127059.1809","DOIUrl":null,"url":null,"abstract":"In this article, we discuss the vertex decomposability of three well-studied simplicial complexes associated to forests. In particular, we show that the bounded degree complex of a forest and the complex of directed trees of a multidiforest is vertex decomposable. We then prove that the non-cover complex of a forest is either contractible or homotopy equivalent to a sphere. Finally we provide a complete characterization of forests whose non-cover complexes are vertex decomposable.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2021.127059.1809","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
In this article, we discuss the vertex decomposability of three well-studied simplicial complexes associated to forests. In particular, we show that the bounded degree complex of a forest and the complex of directed trees of a multidiforest is vertex decomposable. We then prove that the non-cover complex of a forest is either contractible or homotopy equivalent to a sphere. Finally we provide a complete characterization of forests whose non-cover complexes are vertex decomposable.
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