{"title":"A Note on the Number of Triangles in Graphs Without the Suspension of a Path on Four Vertices","authors":"Dániel Gerbner","doi":"10.47443/dml.2022.043","DOIUrl":null,"url":null,"abstract":"The suspension of the path P 4 consists of a P 4 and an additional vertex connected to each of the four vertices, and is denoted by ˆ P 4 . The largest number of triangles in a ˆ P 4 -free n -vertex graph is denoted by ex( n, K 3 , ˆ P 4 ). Mubayi and Mukherjee in 2020 showed that ex( n, K 3 , ˆ P 4 ) = n 2 / 8 + O ( n ). We show that for sufficiently large n , ex( n, K 3 , ˆ P 4 ) = ⌊ n 2 / 8 ⌋ .","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2022-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/dml.2022.043","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
The suspension of the path P 4 consists of a P 4 and an additional vertex connected to each of the four vertices, and is denoted by ˆ P 4 . The largest number of triangles in a ˆ P 4 -free n -vertex graph is denoted by ex( n, K 3 , ˆ P 4 ). Mubayi and Mukherjee in 2020 showed that ex( n, K 3 , ˆ P 4 ) = n 2 / 8 + O ( n ). We show that for sufficiently large n , ex( n, K 3 , ˆ P 4 ) = ⌊ n 2 / 8 ⌋ .
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