Generalized coloring for tree-like graphs
Identifieur interne : 001217 ( Istex/Corpus ); précédent : 001216; suivant : 001218Generalized coloring for tree-like graphs
Auteurs : Klaus Jansen ; Petra SchefflerSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 1993.
Abstract
Abstract: We discuss the Precoloring Extension (PrExt) and the List Coloring (LiCol) problems for trees, partial k-trees and cographs in the decision and the construction versions. Both problems for partial k-trees are solved in linear time, when the number of colors is a constant and by O(¦V¦k+2)-algorithmsin general. For trees, we improve this to linear time. In contrast to that, PrExt and LiCol differ in complexity for cographs. While the first has a linear algorithm, the second is shown NP-complete. We give polynomial algorithms for the corresponding enumeration problems #PrExt and #LiCol on partial k-trees and trees and for #PrExt on cographs.
Url:
DOI: 10.1007/3-540-56402-0_35
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ISTEX:3E9846C912FEE9031CD8FB91675A3364530B426ELe document en format XML
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Both problems for partial k-trees are solved in linear time, when the number of colors is a constant and by O(¦V¦k+2)-algorithmsin general. For trees, we improve this to linear time. In contrast to that, PrExt and LiCol differ in complexity for cographs. While the first has a linear algorithm, the second is shown NP-complete. We give polynomial algorithms for the corresponding enumeration problems #PrExt and #LiCol on partial k-trees and trees and for #PrExt on cographs.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Klaus Jansen</name><affiliations><json:string>FB IV, Universität Trier, Postfach 38 25, D-W-5500, Trier</json:string></affiliations></json:item><json:item><name>Petra Scheffler</name><affiliations><json:string>FB 3, TU Berlin, MA 6-1, Straße des 17. 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We give polynomial algorithms for the corresponding enumeration problems #PrExt and #LiCol on partial k-trees and trees and for #PrExt on cographs.</abstract><qualityIndicators><score>6.224</score><pdfVersion>1.3</pdfVersion><pdfPageSize>439.136 x 666 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>656</abstractCharCount><pdfWordCount>6011</pdfWordCount><pdfCharCount>24071</pdfCharCount><pdfPageCount>10</pdfPageCount><abstractWordCount>102</abstractWordCount></qualityIndicators><title>Generalized coloring for tree-like graphs</title><chapterId><json:string>6</json:string><json:string>Chap6</json:string></chapterId><refBibs><json:item><host><author></author><title>UAr IAi E colset~,l > i > r,A iAAk =O,l >_j C k >r}</title></host></json:item><json:item><author></author><host><pages><first>1</first></pages><author></author><title>If 9 is an union node with children Yl</title></host></json:item><json:item><author><json:item><name>S Arnborg</name></json:item><json:item><name>J Lagergren</name></json:item><json:item><name>D Seese</name></json:item></author><host><pages><last>51</last><first>38</first></pages><author></author><title>Proc. 15th ICALP</title><publicationDate>1988</publicationDate></host><title>Problems easy for tree-decomposable graphs</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>S Arnborg</name></json:item><json:item><name>A Proskurowski</name></json:item></author><host><volume>23</volume><pages><last>24</last><first>11</first></pages><author></author><title>Discr. Appl. Math</title><publicationDate>1989</publicationDate></host><title>Linear-time algorithms for NP-hard problems on graphs embedded in k-trees</title><publicationDate>1989</publicationDate></json:item><json:item><author><json:item><name>M,W Bern</name></json:item><json:item><name>E,L Lawler</name></json:item><json:item><name>A,L Wong</name></json:item></author><host><volume>8</volume><pages><last>235</last><first>216</first></pages><author></author><title>J. Algorithms</title><publicationDate>1987</publicationDate></host><title>Linear-time computations of subgraphs of decomposable graphs</title><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>M Bir6</name></json:item><json:item><name>M Hujter</name></json:item><json:item><name> Zs</name></json:item><json:item><name> Tuza</name></json:item></author><host><author></author><title>Precoloring Extension. I. Interval Graphs. Discrete Math</title></host></json:item><json:item><author><json:item><name>D,G Corneil</name></json:item><json:item><name>Y Perl</name></json:item><json:item><name>L,K Stewart</name></json:item></author><host><volume>4</volume><pages><last>934</last><first>926</first></pages><author></author><title>SIAM J. Comput</title><publicationDate>1985</publicationDate></host><title>A linear recognition algorithm for cographs</title><publicationDate>1985</publicationDate></json:item><json:item><host><author><json:item><name>M,R Garey</name></json:item><json:item><name>D,S Johnson</name></json:item></author><title>Computers and Intractability: A Guide to the Theory of NP-Completeness</title><publicationDate>1979</publicationDate></host></json:item><json:item><author><json:item><name>M Hujter</name></json:item><json:item><name> Zs</name></json:item><json:item><name> Tuza</name></json:item></author><host><author></author><title>J. Graph Theory</title></host><title>Precoloring Extension. II. Graph Classes Related to Bipartite graphs</title></json:item><json:item><author><json:item><name>K Jansen</name></json:item></author><host><author></author><title>Ein Zurdnungproblem im Hardware Design. Dissertation</title><publicationDate>1990</publicationDate></host><publicationDate>1990</publicationDate></json:item><json:item><author><json:item><name>B Reed</name></json:item></author><host><author></author><title>Proc. STOC'92</title><publicationDate>1992</publicationDate></host><title>Finding approximate separators and computing tree-width quickly</title><publicationDate>1992</publicationDate></json:item><json:item><author><json:item><name>N Robertson</name></json:item><json:item><name>P Seymour</name></json:item></author><host><volume>7</volume><pages><last>322</last><first>309</first></pages><author></author><title>J. Algorithms</title><publicationDate>1986</publicationDate></host><title>Graph Minors. II. 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Both problems for partial k-trees are solved in linear time, when the number of colors is a constant and by O(¦V¦k+2)-algorithmsin general. For trees, we improve this to linear time. In contrast to that, PrExt and LiCol differ in complexity for cographs. While the first has a linear algorithm, the second is shown NP-complete. 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graphs</ChapterTitle><ChapterFirstPage>50</ChapterFirstPage><ChapterLastPage>59</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName><CopyrightYear>1993</CopyrightYear></ChapterCopyright><ChapterHistory><OnlineDate><Year>2005</Year><Month>6</Month><Day>4</Day></OnlineDate></ChapterHistory><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><BookID>3540564020</BookID><BookTitle>Graph-Theoretic Concepts in Computer Science</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Klaus</GivenName><FamilyName>Jansen</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Petra</GivenName><FamilyName>Scheffler</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgName>FB IV, Universität Trier</OrgName><OrgAddress><Street>Postfach 38 25</Street><Postcode>D-W-5500</Postcode><City>Trier</City></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>FB 3, TU Berlin, MA 6-1</OrgName><OrgAddress><Street>Straße des 17. Juni 136</Street><Postcode>D-W-1000</Postcode><City>Berlin 12</City></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We discuss the <Emphasis Type="SmallCaps">Precoloring Extension</Emphasis> (<Emphasis Type="SmallCaps">PrExt</Emphasis>) and the <Emphasis Type="SmallCaps">List Coloring</Emphasis> (<Emphasis Type="SmallCaps">LiCol</Emphasis>) problems for trees, partial k-trees and cographs in the decision and the construction versions. Both problems for partial k-trees are solved in linear time, when the number of colors is a constant and by O(¦V¦<Superscript>k+2</Superscript>)-algorithmsin general. For trees, we improve this to linear time. In contrast to that, <Emphasis Type="SmallCaps">PrExt</Emphasis> and <Emphasis Type="SmallCaps">LiCol</Emphasis> differ in complexity for cographs. While the first has a linear algorithm, the second is shown NP-complete. We give polynomial algorithms for the corresponding enumeration problems #<Emphasis Type="SmallCaps">PrExt</Emphasis> and #<Emphasis Type="SmallCaps">LiCol</Emphasis> on partial k-trees and trees and for #<Emphasis Type="SmallCaps">PrExt</Emphasis> on cographs.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>Supported in part by Deutsche Forschungsgemeinschaft</SimplePara></ArticleNote><ArticleNote Type="Misc"><SimplePara>Supported by KAI e. V. under contract 014300/I</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Generalized coloring for tree-like graphs</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Generalized coloring for tree-like graphs</title></titleInfo><name type="personal"><namePart type="given">Klaus</namePart><namePart type="family">Jansen</namePart><affiliation>FB IV, Universität Trier, Postfach 38 25, D-W-5500, Trier</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Petra</namePart><namePart type="family">Scheffler</namePart><affiliation>FB 3, TU Berlin, MA 6-1, Straße des 17. Juni 136, D-W-1000, Berlin 12</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="conference" displayLabel="ReviewPaper"></genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2005-06-04</dateIssued><copyrightDate encoding="w3cdtf">1993</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Abstract: We discuss the Precoloring Extension (PrExt) and the List Coloring (LiCol) problems for trees, partial k-trees and cographs in the decision and the construction versions. Both problems for partial k-trees are solved in linear time, when the number of colors is a constant and by O(¦V¦k+2)-algorithmsin general. For trees, we improve this to linear time. In contrast to that, PrExt and LiCol differ in complexity for cographs. While the first has a linear algorithm, the second is shown NP-complete. We give polynomial algorithms for the corresponding enumeration problems #PrExt and #LiCol on partial k-trees and trees and for #PrExt on cographs.</abstract><relatedItem type="host"><titleInfo><title>Graph-Theoretic Concepts in Computer Science</title><subTitle>18th International Workshop, WG '92 Wiesbaden-Naurod, Germany, June 18–20, 1992 Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Ernst</namePart><namePart type="given">W.</namePart><namePart type="family">Mayr</namePart><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">1993</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I16021">Algorithm Analysis and Problem Complexity</topic><topic authority="SpringerSubjectCodes" authorityURI="M17009">Combinatorics</topic><topic authority="SpringerSubjectCodes" authorityURI="I16013">Computation by Abstract Devices</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic><topic authority="SpringerSubjectCodes" authorityURI="I16048">Mathematical Logic and Formal Languages</topic><topic authority="SpringerSubjectCodes" authorityURI="I15017">Data Structures</topic></subject><identifier type="DOI">10.1007/3-540-56402-0</identifier><identifier type="ISBN">978-3-540-56402-7</identifier><identifier type="eISBN">978-3-540-47554-5</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">33741</identifier><identifier type="BookID">3540564020</identifier><identifier type="BookChapterCount">29</identifier><identifier type="BookVolumeNumber">657</identifier><part><date>1993</date><detail type="volume"><number>657</number><caption>vol.</caption></detail><extent unit="pages"><start>50</start><end>59</end></extent></part><recordInfo><recordOrigin>Springer-Verlag, 1993</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Goos</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Juris</namePart><namePart type="family">Hartmanis</namePart><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><copyrightDate encoding="w3cdtf">1993</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer-Verlag, 1993</recordOrigin></recordInfo></relatedItem><identifier type="istex">3E9846C912FEE9031CD8FB91675A3364530B426E</identifier><identifier type="DOI">10.1007/3-540-56402-0_35</identifier><identifier type="ChapterID">6</identifier><identifier type="ChapterID">Chap6</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 1993</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag, 1993</recordOrigin></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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