{"title":"关于随机图中的诱导路径、洞和树","authors":"Kunal Dutta, C. Subramanian","doi":"10.1137/1.9781611975062.15","DOIUrl":null,"url":null,"abstract":"We study the concentration of the largest induced paths, trees and cycles (holes) in the Erdos-Renyi random graph model and prove a 2-point concentration for the size of the largest induced path and hole, for all p = Ω(n ln n). As a corollary, we obtain an improvement over a result of Erdos and Palka concerning the size of the largest induced tree in a random graph. Further, we study the path chromatic number and tree chromatic number i.e. the smallest number of parts into which the vertex set of a graph can be partitioned such that every The arguments involve the application of a modified version of a probabilistic inequality of Krivelevich, Sudakov, Vu and Wormald.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":"55 1","pages":"279-303"},"PeriodicalIF":0.0000,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"On Induced Paths, Holes and Trees in Random Graphs\",\"authors\":\"Kunal Dutta, C. Subramanian\",\"doi\":\"10.1137/1.9781611975062.15\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the concentration of the largest induced paths, trees and cycles (holes) in the Erdos-Renyi random graph model and prove a 2-point concentration for the size of the largest induced path and hole, for all p = Ω(n ln n). As a corollary, we obtain an improvement over a result of Erdos and Palka concerning the size of the largest induced tree in a random graph. Further, we study the path chromatic number and tree chromatic number i.e. the smallest number of parts into which the vertex set of a graph can be partitioned such that every The arguments involve the application of a modified version of a probabilistic inequality of Krivelevich, Sudakov, Vu and Wormald.\",\"PeriodicalId\":21749,\"journal\":{\"name\":\"SIAM J. Discret. Math.\",\"volume\":\"55 1\",\"pages\":\"279-303\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM J. Discret. Math.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/1.9781611975062.15\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM J. Discret. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/1.9781611975062.15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On Induced Paths, Holes and Trees in Random Graphs
We study the concentration of the largest induced paths, trees and cycles (holes) in the Erdos-Renyi random graph model and prove a 2-point concentration for the size of the largest induced path and hole, for all p = Ω(n ln n). As a corollary, we obtain an improvement over a result of Erdos and Palka concerning the size of the largest induced tree in a random graph. Further, we study the path chromatic number and tree chromatic number i.e. the smallest number of parts into which the vertex set of a graph can be partitioned such that every The arguments involve the application of a modified version of a probabilistic inequality of Krivelevich, Sudakov, Vu and Wormald.