Deepak Bal, Patrick Bennett, Sean English, Calum MacRury, P. Prałat
{"title":"随机正则图中的零强迫","authors":"Deepak Bal, Patrick Bennett, Sean English, Calum MacRury, P. Prałat","doi":"10.4310/joc.2021.v12.n1.a4","DOIUrl":null,"url":null,"abstract":"The zero forcing process is an iterative graph colouring process in which at each time step a coloured vertex with a single uncoloured neighbour can force this neighbour to become coloured. A zero forcing set of a graph is an initial set of coloured vertices that can eventually force the entire graph to be coloured. The zero forcing number is the size of the smallest zero forcing set. We explore the zero forcing number for random regular graphs, improving on bounds given by Kalinowski, Kam˘cev and Sudakov [15]. We also propose and analyze a degree greedy algorithm for finding small zero forcing sets using the differential equations method.","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"12 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Zero-forcing in random regular graphs\",\"authors\":\"Deepak Bal, Patrick Bennett, Sean English, Calum MacRury, P. Prałat\",\"doi\":\"10.4310/joc.2021.v12.n1.a4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The zero forcing process is an iterative graph colouring process in which at each time step a coloured vertex with a single uncoloured neighbour can force this neighbour to become coloured. A zero forcing set of a graph is an initial set of coloured vertices that can eventually force the entire graph to be coloured. The zero forcing number is the size of the smallest zero forcing set. We explore the zero forcing number for random regular graphs, improving on bounds given by Kalinowski, Kam˘cev and Sudakov [15]. We also propose and analyze a degree greedy algorithm for finding small zero forcing sets using the differential equations method.\",\"PeriodicalId\":44683,\"journal\":{\"name\":\"Journal of Combinatorics\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/joc.2021.v12.n1.a4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/joc.2021.v12.n1.a4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
The zero forcing process is an iterative graph colouring process in which at each time step a coloured vertex with a single uncoloured neighbour can force this neighbour to become coloured. A zero forcing set of a graph is an initial set of coloured vertices that can eventually force the entire graph to be coloured. The zero forcing number is the size of the smallest zero forcing set. We explore the zero forcing number for random regular graphs, improving on bounds given by Kalinowski, Kam˘cev and Sudakov [15]. We also propose and analyze a degree greedy algorithm for finding small zero forcing sets using the differential equations method.
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