{"title":"在对数空间中列出着色树","authors":"H. Bodlaender, C. Groenland, Hugo Jacob","doi":"10.48550/arXiv.2206.09750","DOIUrl":null,"url":null,"abstract":"We show that List Colouring can be solved on n -vertex trees by a deterministic Turing machine using O (log n ) bits on the worktape. Given an n -vertex graph G = ( V, E ) and a list L ( v ) ⊆ { 1 , . . . , n } of available colours for each v ∈ V , a list colouring for G is a proper colouring c such that c ( v ) ∈ L ( v ) for all v .","PeriodicalId":201778,"journal":{"name":"Embedded Systems and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"List Colouring Trees in Logarithmic Space\",\"authors\":\"H. Bodlaender, C. Groenland, Hugo Jacob\",\"doi\":\"10.48550/arXiv.2206.09750\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that List Colouring can be solved on n -vertex trees by a deterministic Turing machine using O (log n ) bits on the worktape. Given an n -vertex graph G = ( V, E ) and a list L ( v ) ⊆ { 1 , . . . , n } of available colours for each v ∈ V , a list colouring for G is a proper colouring c such that c ( v ) ∈ L ( v ) for all v .\",\"PeriodicalId\":201778,\"journal\":{\"name\":\"Embedded Systems and Applications\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Embedded Systems and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2206.09750\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Embedded Systems and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2206.09750","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We show that List Colouring can be solved on n -vertex trees by a deterministic Turing machine using O (log n ) bits on the worktape. Given an n -vertex graph G = ( V, E ) and a list L ( v ) ⊆ { 1 , . . . , n } of available colours for each v ∈ V , a list colouring for G is a proper colouring c such that c ( v ) ∈ L ( v ) for all v .
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