{"title":"适当圆弧图的全着色和边着色","authors":"J. Bernardi, S. M. Almeida, L. M. Zatesko","doi":"10.5753/ETC.2018.3557","DOIUrl":null,"url":null,"abstract":"Deciding if a graph is Δ-edge-colourable (resp. (Δ + 1)-total colourable), although it is an NP-complete problem for graphs in general, is polynomially solvable for interval graphs of odd (resp. even) maximum degree Δ. An interesting superclass of the proper interval graphs are the proper circular-arc graphs, for which we suspect that Δ-edge-colourability is linear-time decidable. This work presents sufficient conditions for Δ-edge-colourability, (Δ + 1)-total colourability, and (Δ+2)-total colourability of proper circular-arc graphs. Our proofs are constructive and yield polynomial-time algorithms.","PeriodicalId":315906,"journal":{"name":"Anais do Encontro de Teoria da Computação (ETC)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On Total and Edge-colouring of Proper Circular-arc Graphs\",\"authors\":\"J. Bernardi, S. M. Almeida, L. M. Zatesko\",\"doi\":\"10.5753/ETC.2018.3557\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Deciding if a graph is Δ-edge-colourable (resp. (Δ + 1)-total colourable), although it is an NP-complete problem for graphs in general, is polynomially solvable for interval graphs of odd (resp. even) maximum degree Δ. An interesting superclass of the proper interval graphs are the proper circular-arc graphs, for which we suspect that Δ-edge-colourability is linear-time decidable. This work presents sufficient conditions for Δ-edge-colourability, (Δ + 1)-total colourability, and (Δ+2)-total colourability of proper circular-arc graphs. Our proofs are constructive and yield polynomial-time algorithms.\",\"PeriodicalId\":315906,\"journal\":{\"name\":\"Anais do Encontro de Teoria da Computação (ETC)\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Anais do Encontro de Teoria da Computação (ETC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5753/ETC.2018.3557\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Anais do Encontro de Teoria da Computação (ETC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5753/ETC.2018.3557","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On Total and Edge-colouring of Proper Circular-arc Graphs
Deciding if a graph is Δ-edge-colourable (resp. (Δ + 1)-total colourable), although it is an NP-complete problem for graphs in general, is polynomially solvable for interval graphs of odd (resp. even) maximum degree Δ. An interesting superclass of the proper interval graphs are the proper circular-arc graphs, for which we suspect that Δ-edge-colourability is linear-time decidable. This work presents sufficient conditions for Δ-edge-colourability, (Δ + 1)-total colourability, and (Δ+2)-total colourability of proper circular-arc graphs. Our proofs are constructive and yield polynomial-time algorithms.
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