{"title":"若干正则图的游戏色数","authors":"Ramy S. Shaheen, Z. Kanaya, Khaled Alshehada","doi":"10.4236/ojdm.2019.94012","DOIUrl":null,"url":null,"abstract":"Let G be a graph and k be a positive integer. We consider a game with two players Alice and Bob who alternate in coloring the vertices of G with a set of k colors. In every turn, one vertex will be chosen by one player. Alice’s goal is to color all vertices with the k colors, while Bob’s goal is to prevent her. The game chromatic number denoted by χg(G), is the smallest k such that Alice has a winning strategy with k colors. In this paper, we determine the game chromatic number χg of circulant graphs Cn(1,2), , and generalized Petersen graphs GP(n,2), GP(n,3).","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Game Chromatic Number of Some Regular Graphs\",\"authors\":\"Ramy S. Shaheen, Z. Kanaya, Khaled Alshehada\",\"doi\":\"10.4236/ojdm.2019.94012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let G be a graph and k be a positive integer. We consider a game with two players Alice and Bob who alternate in coloring the vertices of G with a set of k colors. In every turn, one vertex will be chosen by one player. Alice’s goal is to color all vertices with the k colors, while Bob’s goal is to prevent her. The game chromatic number denoted by χg(G), is the smallest k such that Alice has a winning strategy with k colors. In this paper, we determine the game chromatic number χg of circulant graphs Cn(1,2), , and generalized Petersen graphs GP(n,2), GP(n,3).\",\"PeriodicalId\":61712,\"journal\":{\"name\":\"离散数学期刊(英文)\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-08-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"离散数学期刊(英文)\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.4236/ojdm.2019.94012\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"离散数学期刊(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/ojdm.2019.94012","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let G be a graph and k be a positive integer. We consider a game with two players Alice and Bob who alternate in coloring the vertices of G with a set of k colors. In every turn, one vertex will be chosen by one player. Alice’s goal is to color all vertices with the k colors, while Bob’s goal is to prevent her. The game chromatic number denoted by χg(G), is the smallest k such that Alice has a winning strategy with k colors. In this paper, we determine the game chromatic number χg of circulant graphs Cn(1,2), , and generalized Petersen graphs GP(n,2), GP(n,3).
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