{"title":"Recognizing shrinkable complexes is NP-complete","authors":"D. Attali, O. Devillers, M. Glisse, S. Lazard","doi":"10.20382/jocg.v7i1a18","DOIUrl":null,"url":null,"abstract":"We say that a simplicial complex is shrinkable if there exists a sequence of admissible edge contractions that reduces the complex to a single vertex. We prove that it is NP-complete to decide whether a (three-dimensional) simplicial complex is shrinkable. Along the way, we describe examples of contractible complexes which are not shrinkable.","PeriodicalId":43044,"journal":{"name":"Journal of Computational Geometry","volume":"657 1","pages":"74-86"},"PeriodicalIF":0.4000,"publicationDate":"2014-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.20382/jocg.v7i1a18","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 6
Abstract
We say that a simplicial complex is shrinkable if there exists a sequence of admissible edge contractions that reduces the complex to a single vertex. We prove that it is NP-complete to decide whether a (three-dimensional) simplicial complex is shrinkable. Along the way, we describe examples of contractible complexes which are not shrinkable.
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