Generalized coloring for tree-like graphs
Identifieur interne : 001270 ( Istex/Corpus ); précédent : 001269; suivant : 001271Generalized coloring for tree-like graphs
Auteurs : Klaus Jansen ; Petra SchefflerSource :
- Discrete Applied Mathematics [ 0166-218X ] ; 1997.
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 bounded by a constant and in polynomial time for an unbounded number of colors. For trees, we improve this to linear time. In contrast to that, the two problems differ in complexity for cographs. While PrExt has a linear-time decision algorithm, LiCol is shown to be NP-complete. We give polynomial-time algorithms for the corresponding enumeration problems # PrExt and # LiCol on partial k-trees and trees and for # PrExt on cographs.
Url:
DOI: 10.1016/S0166-218X(96)00085-6
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Both problems for partial k-trees are solved in linear time when the number of colors is bounded by a constant and in polynomial time for an unbounded number of colors. For trees, we improve this to linear time. In contrast to that, the two problems differ in complexity for cographs. While PrExt has a linear-time decision algorithm, LiCol is shown to be NP-complete. We give polynomial-time 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>elsevier</corpusName><author><json:item><name>Klaus Jansen</name><affiliations><json:string>E-mail: jansen@dm3.uni-trier.de</json:string><json:string>FB IV — Mathematik und Informatik, Universität Trier, Postfach 38 25, D-54286 Trier, Germany</json:string></affiliations></json:item><json:item><name>Petra Scheffler</name><affiliations><json:string>Fachbereich Wirtschaft, Fachhochschule Stralsund, Groβe Parower Straβe 145, D-18435 Stralsund, Germany</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><originalGenre><json:string>Full-length article</json:string></originalGenre><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 bounded by a constant and in polynomial time for an unbounded number of colors. For trees, we improve this to linear time. In contrast to that, the two problems differ in complexity for cographs. While PrExt has a linear-time decision algorithm, LiCol is shown to be NP-complete. We give polynomial-time algorithms for the corresponding enumeration problems # PrExt and # LiCol on partial k-trees and trees and for # PrExt on cographs.</abstract><qualityIndicators><score>6.356</score><pdfVersion>1.2</pdfVersion><pdfPageSize>468 x 684 pts</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>695</abstractCharCount><pdfWordCount>9072</pdfWordCount><pdfCharCount>43867</pdfCharCount><pdfPageCount>21</pdfPageCount><abstractWordCount>113</abstractWordCount></qualityIndicators><title>Generalized coloring for tree-like graphs</title><pii><json:string>S0166-218X(96)00085-6</json:string></pii><refBibs><json:item><host><author></author><title>The design and analysis of computer algorithms</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. 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Analiz</title></host><title>Critical graphs with given chromatic class (Russian)</title></json:item></refBibs><genre><json:string>research-article</json:string></genre><serie><pages><last>51</last><first>38</first></pages><language><json:string>unknown</json:string></language><title>Proc. 15th ICALP</title></serie><host><volume>75</volume><pii><json:string>S0166-218X(00)X0042-X</json:string></pii><pages><last>155</last><first>135</first></pages><issn><json:string>0166-218X</json:string></issn><issue>2</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><title>Discrete Applied Mathematics</title><publicationDate>1997</publicationDate></host><categories><wos><json:string>science</json:string><json:string>mathematics, applied</json:string></wos><scienceMetrix><json:string>applied sciences</json:string><json:string>information & communication technologies</json:string><json:string>computation theory & mathematics</json:string></scienceMetrix></categories><publicationDate>1997</publicationDate><copyrightDate>1997</copyrightDate><doi><json:string>10.1016/S0166-218X(96)00085-6</json:string></doi><id>B786DB27747FE60A5EF8B582C4EBFCCFEEA2D041</id><score>0.4828148</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/B786DB27747FE60A5EF8B582C4EBFCCFEEA2D041/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/B786DB27747FE60A5EF8B582C4EBFCCFEEA2D041/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/B786DB27747FE60A5EF8B582C4EBFCCFEEA2D041/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">Generalized coloring for tree-like graphs</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>ELSEVIER</publisher><availability><p>ELSEVIER</p></availability><date>1997</date></publicationStmt><notesStmt><note type="content">Section title: Contribution</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">Generalized coloring for tree-like graphs</title><author xml:id="author-1"><persName><forename type="first">Klaus</forename><surname>Jansen</surname></persName><email>jansen@dm3.uni-trier.de</email><note type="biography">Supported in part by Deutsche Forschungsgemeinschaft.</note><note type="correspondence"><p>Corresponding author.</p></note><affiliation>Supported in part by Deutsche Forschungsgemeinschaft.</affiliation><affiliation>FB IV — Mathematik und Informatik, Universität Trier, Postfach 38 25, D-54286 Trier, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">Petra</forename><surname>Scheffler</surname></persName><note type="biography">Supported by Koordinierungs- und Aufbau-Initiative für die Forschung in den Ländern Berlin, Brandenburg, Mecklenburg-Vorpommern, Sachsen, Sachsen-Anhalt und Thüringen e.V. under contract 014300/I.</note><affiliation>Supported by Koordinierungs- und Aufbau-Initiative für die Forschung in den Ländern Berlin, Brandenburg, Mecklenburg-Vorpommern, Sachsen, Sachsen-Anhalt und Thüringen e.V. under contract 014300/I.</affiliation><affiliation>Fachbereich Wirtschaft, Fachhochschule Stralsund, Groβe Parower Straβe 145, D-18435 Stralsund, Germany</affiliation></author></analytic><monogr><title level="j">Discrete Applied Mathematics</title><title level="j" type="abbrev">DAM</title><idno type="pISSN">0166-218X</idno><idno type="PII">S0166-218X(00)X0042-X</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1997"></date><biblScope unit="volume">75</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="135">135</biblScope><biblScope unit="page" to="155">155</biblScope></imprint></monogr><idno type="istex">B786DB27747FE60A5EF8B582C4EBFCCFEEA2D041</idno><idno type="DOI">10.1016/S0166-218X(96)00085-6</idno><idno type="PII">S0166-218X(96)00085-6</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1997</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>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 bounded by a constant and in polynomial time for an unbounded number of colors. For trees, we improve this to linear time. In contrast to that, the two problems differ in complexity for cographs. While PrExt has a linear-time decision algorithm, LiCol is shown to be NP-complete. We give polynomial-time algorithms for the corresponding enumeration problems # PrExt and # LiCol on partial k-trees and trees and for # PrExt on cographs.</p></abstract></profileDesc><revisionDesc><change when="1992-05-15">Modified</change><change when="1997">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/B786DB27747FE60A5EF8B582C4EBFCCFEEA2D041/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: tail"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>DAM</jid><aid>96000856</aid><ce:pii>S0166-218X(96)00085-6</ce:pii><ce:doi>10.1016/S0166-218X(96)00085-6</ce:doi><ce:copyright type="unknown" year="1997"></ce:copyright></item-info><head><ce:dochead><ce:textfn>Contribution</ce:textfn></ce:dochead><ce:title>Generalized coloring for tree-like graphs</ce:title><ce:author-group><ce:author><ce:given-name>Klaus</ce:given-name><ce:surname>Jansen</ce:surname><ce:cross-ref refid="COR1"><ce:sup>∗</ce:sup></ce:cross-ref><ce:cross-ref refid="AFF1"><ce:sup>a</ce:sup></ce:cross-ref><ce:cross-ref refid="FN1"><ce:sup>1</ce:sup></ce:cross-ref><ce:e-address>jansen@dm3.uni-trier.de</ce:e-address></ce:author><ce:author><ce:given-name>Petra</ce:given-name><ce:surname>Scheffler</ce:surname><ce:cross-ref refid="AFF2"><ce:sup>b</ce:sup></ce:cross-ref><ce:cross-ref refid="FN2"><ce:sup>2</ce:sup></ce:cross-ref></ce:author><ce:affiliation id="AFF1"><ce:label>a</ce:label><ce:textfn>FB IV — Mathematik und Informatik, Universität Trier, Postfach 38 25, D-54286 Trier, Germany</ce:textfn></ce:affiliation><ce:affiliation id="AFF2"><ce:label>b</ce:label><ce:textfn>Fachbereich Wirtschaft, Fachhochschule Stralsund, Groβe Parower Straβe 145, D-18435 Stralsund, Germany</ce:textfn></ce:affiliation><ce:correspondence id="COR1"><ce:label>∗</ce:label><ce:text>Corresponding author.</ce:text></ce:correspondence><ce:footnote id="FN1"><ce:label>1</ce:label><ce:note-para>Supported in part by Deutsche Forschungsgemeinschaft.</ce:note-para></ce:footnote><ce:footnote id="FN2"><ce:label>2</ce:label><ce:note-para>Supported by Koordinierungs- und Aufbau-Initiative für die Forschung in den Ländern Berlin, Brandenburg, Mecklenburg-Vorpommern, Sachsen, Sachsen-Anhalt und Thüringen e.V. under contract 014300/I.</ce:note-para></ce:footnote></ce:author-group><ce:date-received day="31" month="3" year="1992"></ce:date-received><ce:date-revised day="15" month="5" year="1992"></ce:date-revised><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>We discuss the <ce:small-caps>Precoloring Extension</ce:small-caps> (<ce:small-caps>PrExt</ce:small-caps>) and the <ce:small-caps>List Coloring</ce:small-caps> (<ce:small-caps>LiCol</ce:small-caps>) problems for trees, partial <ce:italic>k</ce:italic>-trees and cographs in the decision and the construction versions. Both problems for partial <ce:italic>k</ce:italic>-trees are solved in linear time when the number of colors is bounded by a constant and in polynomial time for an unbounded number of colors. For trees, we improve this to linear time. In contrast to that, the two problems differ in complexity for cographs. While <ce:small-caps>PrExt</ce:small-caps> has a linear-time decision algorithm, <ce:small-caps>LiCol</ce:small-caps> is shown to be NP-complete. We give polynomial-time algorithms for the corresponding enumeration problems # <ce:small-caps>PrExt</ce:small-caps> and # <ce:small-caps>LiCol</ce:small-caps> on partial <ce:italic>k</ce:italic>-trees and trees and for # <ce:small-caps>PrExt</ce:small-caps> on cographs.</ce:simple-para></ce:abstract-sec></ce:abstract></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Generalized coloring for tree-like graphs</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Generalized coloring for tree-like graphs</title></titleInfo><name type="personal"><namePart type="given">Klaus</namePart><namePart type="family">Jansen</namePart><affiliation>E-mail: jansen@dm3.uni-trier.de</affiliation><affiliation>FB IV — Mathematik und Informatik, Universität Trier, Postfach 38 25, D-54286 Trier, Germany</affiliation><description>Corresponding author.</description><description>Supported in part by Deutsche Forschungsgemeinschaft.</description><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Petra</namePart><namePart type="family">Scheffler</namePart><affiliation>Fachbereich Wirtschaft, Fachhochschule Stralsund, Groβe Parower Straβe 145, D-18435 Stralsund, Germany</affiliation><description>Supported by Koordinierungs- und Aufbau-Initiative für die Forschung in den Ländern Berlin, Brandenburg, Mecklenburg-Vorpommern, Sachsen, Sachsen-Anhalt und Thüringen e.V. under contract 014300/I.</description><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">1997</dateIssued><dateModified encoding="w3cdtf">1992-05-15</dateModified><copyrightDate encoding="w3cdtf">1997</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">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 bounded by a constant and in polynomial time for an unbounded number of colors. For trees, we improve this to linear time. In contrast to that, the two problems differ in complexity for cographs. While PrExt has a linear-time decision algorithm, LiCol is shown to be NP-complete. We give polynomial-time algorithms for the corresponding enumeration problems # PrExt and # LiCol on partial k-trees and trees and for # PrExt on cographs.</abstract><note type="content">Section title: Contribution</note><relatedItem type="host"><titleInfo><title>Discrete Applied Mathematics</title></titleInfo><titleInfo type="abbreviated"><title>DAM</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">19970530</dateIssued></originInfo><identifier type="ISSN">0166-218X</identifier><identifier type="PII">S0166-218X(00)X0042-X</identifier><part><date>19970530</date><detail type="volume"><number>75</number><caption>vol.</caption></detail><detail type="issue"><number>2</number><caption>no.</caption></detail><extent unit="issue pages"><start>105</start><end>200</end></extent><extent unit="pages"><start>135</start><end>155</end></extent></part></relatedItem><identifier type="istex">B786DB27747FE60A5EF8B582C4EBFCCFEEA2D041</identifier><identifier type="DOI">10.1016/S0166-218X(96)00085-6</identifier><identifier type="PII">S0166-218X(96)00085-6</identifier><recordInfo><recordContentSource>ELSEVIER</recordContentSource></recordInfo></mods></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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