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
Links to Exploration step
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<front><div type="abstract" xml: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.</div>
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<BookTitle>Graph-Theoretic Concepts in Computer Science</BookTitle>
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<ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Klaus</GivenName>
<FamilyName>Jansen</FamilyName>
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<Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Petra</GivenName>
<FamilyName>Scheffler</FamilyName>
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<Affiliation ID="Aff1"><OrgName>FB IV, Universität Trier</OrgName>
<OrgAddress><Street>Postfach 38 25</Street>
<Postcode>D-W-5500</Postcode>
<City>Trier</City>
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<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>
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<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>
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<mods version="3.6"><titleInfo lang="en"><title>Generalized coloring for tree-like graphs</title>
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<titleInfo type="alternative" contentType="CDATA" lang="en"><title>Generalized coloring for tree-like graphs</title>
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<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>
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<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>
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<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>
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<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>
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<originInfo><copyrightDate encoding="w3cdtf">1993</copyrightDate>
<issuance>monographic</issuance>
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<subject><genre>Book-Subject-Collection</genre>
<topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic>
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<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>
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<part><date>1993</date>
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<caption>vol.</caption>
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<extent unit="pages"><start>50</start>
<end>59</end>
</extent>
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<relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title>
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<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>
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