{"title":"Turán跨越星林的数量","authors":"Lin-Peng Zhang, Ligong Wang, Jiale Zhou","doi":"10.7151/dmgt.2368","DOIUrl":null,"url":null,"abstract":"Let F be a family of graphs. The Turán number of F , denoted by ex(n,F), is the maximum number of edges in a graph with n vertices which does not contain any subgraph isomorphic to some graph in F . A star forest is a forest whose connected components are all stars and isolated vertices. Motivated by the results of Wang, Yang and Ning about the spanning Turán number of linear forests [J. Wang and W. Yang, The Turán number for spanning linear forests, Discrete Appl. Math. 254 (2019) 291–294; B. Ning and J. Wang, The formula for Turán number of spanning linear forests, Discrete Math. 343 (2020) 111924]. In this paper, let Sn,k be the set of all star forests with n vertices and k edges. We prove that when 1 ≤ k ≤ n− 1, ex(n,Sn,k) = ⌊ k−1 2 ⌋ .","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The Turán number of spanning star forests\",\"authors\":\"Lin-Peng Zhang, Ligong Wang, Jiale Zhou\",\"doi\":\"10.7151/dmgt.2368\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let F be a family of graphs. The Turán number of F , denoted by ex(n,F), is the maximum number of edges in a graph with n vertices which does not contain any subgraph isomorphic to some graph in F . A star forest is a forest whose connected components are all stars and isolated vertices. Motivated by the results of Wang, Yang and Ning about the spanning Turán number of linear forests [J. Wang and W. Yang, The Turán number for spanning linear forests, Discrete Appl. Math. 254 (2019) 291–294; B. Ning and J. Wang, The formula for Turán number of spanning linear forests, Discrete Math. 343 (2020) 111924]. In this paper, let Sn,k be the set of all star forests with n vertices and k edges. We prove that when 1 ≤ k ≤ n− 1, ex(n,Sn,k) = ⌊ k−1 2 ⌋ .\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7151/dmgt.2368\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7151/dmgt.2368","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let F be a family of graphs. The Turán number of F , denoted by ex(n,F), is the maximum number of edges in a graph with n vertices which does not contain any subgraph isomorphic to some graph in F . A star forest is a forest whose connected components are all stars and isolated vertices. Motivated by the results of Wang, Yang and Ning about the spanning Turán number of linear forests [J. Wang and W. Yang, The Turán number for spanning linear forests, Discrete Appl. Math. 254 (2019) 291–294; B. Ning and J. Wang, The formula for Turán number of spanning linear forests, Discrete Math. 343 (2020) 111924]. In this paper, let Sn,k be the set of all star forests with n vertices and k edges. We prove that when 1 ≤ k ≤ n− 1, ex(n,Sn,k) = ⌊ k−1 2 ⌋ .
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