{"title":"The number of cliques in hypergraphs with forbidden subgraphs","authors":"Ayush Basu , Vojtěch Rödl , Yi Zhao","doi":"10.1016/j.disc.2025.114415","DOIUrl":null,"url":null,"abstract":"<div><div>We study the maximum number of <em>r</em>-vertex cliques in <span><math><mo>(</mo><mi>r</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-uniform hypergraphs not containing complete <em>r</em>-partite hypergraphs <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow><mrow><mo>(</mo><mi>r</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msubsup><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>)</mo></math></span>. By using the hypergraph removal lemma, we show that this maximum is <span><math><mi>o</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn><mo>/</mo><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>)</mo></mrow></msup><mo>)</mo></math></span>. This immediately implies the corresponding results of Mubayi and Mukherjee and of Balogh, Jiang, and Luo for graphs. We also provide a lower bound by using hypergraph Turán numbers.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 5","pages":"Article 114415"},"PeriodicalIF":0.7000,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X25000238","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the maximum number of r-vertex cliques in -uniform hypergraphs not containing complete r-partite hypergraphs . By using the hypergraph removal lemma, we show that this maximum is . This immediately implies the corresponding results of Mubayi and Mukherjee and of Balogh, Jiang, and Luo for graphs. We also provide a lower bound by using hypergraph Turán numbers.
期刊介绍：
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
