{"title":"Minimal asymmetric hypergraphs","authors":"Yiting Jiang , Jaroslav Nešetřil","doi":"10.1016/j.jctb.2023.08.006","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we prove that for any <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span>, there exist infinitely many minimal asymmetric <em>k</em><span>-uniform hypergraphs. This is in a striking contrast to </span><span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>, where it has been proved recently that there are exactly 18 minimal asymmetric graphs.</p><p>We also determine, for every <span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span>, the minimum size of an asymmetric <em>k</em>-uniform hypergraph.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"164 ","pages":"Pages 105-118"},"PeriodicalIF":1.2000,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series B","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0095895623000667","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we prove that for any , there exist infinitely many minimal asymmetric k-uniform hypergraphs. This is in a striking contrast to , where it has been proved recently that there are exactly 18 minimal asymmetric graphs.
We also determine, for every , the minimum size of an asymmetric k-uniform hypergraph.
期刊介绍：
The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.
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