{"title":"极小非对称超图","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":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"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\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-09-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0095895623000667\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0095895623000667","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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