{"title":"展开k页图","authors":"Ravi Kannan","doi":"10.1016/S0019-9958(85)80008-5","DOIUrl":null,"url":null,"abstract":"<div><p>I show in this note that for any integer <em>k</em> and any <em>k</em> page graph <em>G</em>, there is an easily constructed 3-page graph <em>G</em>′ (called the unraveling of <em>G</em>) such that the minimum separator sizes of <em>G</em> and <em>G</em>′ are within a factor of <em>k</em> of each other. Further the maximum degree of a vertex of <em>G</em>′ is at most 2 plus the maximum degree of <em>G</em>.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":"66 1","pages":"Pages 1-5"},"PeriodicalIF":0.0000,"publicationDate":"1985-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(85)80008-5","citationCount":"14","resultStr":"{\"title\":\"Unraveling k-page graphs\",\"authors\":\"Ravi Kannan\",\"doi\":\"10.1016/S0019-9958(85)80008-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>I show in this note that for any integer <em>k</em> and any <em>k</em> page graph <em>G</em>, there is an easily constructed 3-page graph <em>G</em>′ (called the unraveling of <em>G</em>) such that the minimum separator sizes of <em>G</em> and <em>G</em>′ are within a factor of <em>k</em> of each other. Further the maximum degree of a vertex of <em>G</em>′ is at most 2 plus the maximum degree of <em>G</em>.</p></div>\",\"PeriodicalId\":38164,\"journal\":{\"name\":\"信息与控制\",\"volume\":\"66 1\",\"pages\":\"Pages 1-5\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1985-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0019-9958(85)80008-5\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"信息与控制\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019995885800085\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995885800085","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
I show in this note that for any integer k and any k page graph G, there is an easily constructed 3-page graph G′ (called the unraveling of G) such that the minimum separator sizes of G and G′ are within a factor of k of each other. Further the maximum degree of a vertex of G′ is at most 2 plus the maximum degree of G.
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