{"title":"关于平面图形dp着色不当的一个注记","authors":"Hongyan Cai, Qiang Sun","doi":"10.1080/23799927.2021.1872707","DOIUrl":null,"url":null,"abstract":"ABSTRACT DP-colouring (also known as correspondence colouring), introduced by Dvořák and Postle, is a generalization of list colouring. Many results on list-colouring of graphs, especially of planar graphs, have been extended to the setting of DP-colouring. Recently, Pongpat and Kittikorn [P. Sittitrai and K. Nakprasit, Suffficient conditions on planar graphs to have a relaxed DP-3-colourability, Graphs and Combinatorics 35 (2019), pp. 837–845.] introduced DP- -colouring to generalize -colouring and -choosability. They proved that every planar graph G without -cycles is DP- -colourable. In this note, we show the following results:(1) Every planar graph G without -cycles is DP- -colourable; (2) Every planar graph G without -cycles is DP- -colourable; (3) Every planar graph G without -cycles is DP- -colourable.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2021-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on improper DP-colouring of planar graphs\",\"authors\":\"Hongyan Cai, Qiang Sun\",\"doi\":\"10.1080/23799927.2021.1872707\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"ABSTRACT DP-colouring (also known as correspondence colouring), introduced by Dvořák and Postle, is a generalization of list colouring. Many results on list-colouring of graphs, especially of planar graphs, have been extended to the setting of DP-colouring. Recently, Pongpat and Kittikorn [P. Sittitrai and K. Nakprasit, Suffficient conditions on planar graphs to have a relaxed DP-3-colourability, Graphs and Combinatorics 35 (2019), pp. 837–845.] introduced DP- -colouring to generalize -colouring and -choosability. They proved that every planar graph G without -cycles is DP- -colourable. In this note, we show the following results:(1) Every planar graph G without -cycles is DP- -colourable; (2) Every planar graph G without -cycles is DP- -colourable; (3) Every planar graph G without -cycles is DP- -colourable.\",\"PeriodicalId\":37216,\"journal\":{\"name\":\"International Journal of Computer Mathematics: Computer Systems Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-01-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Computer Mathematics: Computer Systems Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/23799927.2021.1872707\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computer Mathematics: Computer Systems Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/23799927.2021.1872707","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
ABSTRACT DP-colouring (also known as correspondence colouring), introduced by Dvořák and Postle, is a generalization of list colouring. Many results on list-colouring of graphs, especially of planar graphs, have been extended to the setting of DP-colouring. Recently, Pongpat and Kittikorn [P. Sittitrai and K. Nakprasit, Suffficient conditions on planar graphs to have a relaxed DP-3-colourability, Graphs and Combinatorics 35 (2019), pp. 837–845.] introduced DP- -colouring to generalize -colouring and -choosability. They proved that every planar graph G without -cycles is DP- -colourable. In this note, we show the following results:(1) Every planar graph G without -cycles is DP- -colourable; (2) Every planar graph G without -cycles is DP- -colourable; (3) Every planar graph G without -cycles is DP- -colourable.
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