Generalized coloring for tree-like graphs
Identifieur interne : 001052 ( PascalFrancis/Checkpoint ); précédent : 001051; suivant : 001053Generalized coloring for tree-like graphs
Auteurs : K. Jansen [Allemagne] ; P. Scheffler [Allemagne]Source :
- Discrete applied mathematics [ 0166-218X ] ; 1997.
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Abstract
Copyright (c) 1997 Elsevier Science B.V. All rights reserved. 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.
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All rights reserved. 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.</div></front></TEI><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0166-218X</s0></fA01><fA02 i1="01"><s0>DAMADU</s0></fA02><fA03 i2="1"><s0>Discrete appl. math.</s0></fA03><fA05><s2>75</s2></fA05><fA06><s2>2</s2></fA06><fA08 i1="01" i2="1" l="ENG"><s1>Generalized coloring for tree-like graphs</s1></fA08><fA11 i1="01" i2="1"><s1>JANSEN (K.)</s1></fA11><fA11 i1="02" i2="1"><s1>SCHEFFLER (P.)</s1></fA11><fA14 i1="01"><s1>FB IV - Mathematik und Informatik, Universität Trier, Postfach 38 25</s1><s2>D-54286 Trier</s2><s3>DEU</s3><sZ>1 aut.</sZ></fA14><fA14 i1="02"><s1>Fachbereich Wirtschaft, Fachhochschule Stralsund, Groe Parower Strae 145</s1><s2>D-18435 Stralsund</s2><s3>DEU</s3><sZ>2 aut.</sZ></fA14><fA20><s1>135-155</s1></fA20><fA21><s1>1997</s1></fA21><fA23 i1="01"><s0>ENG</s0></fA23><fA24 i1="01"><s0>eng</s0></fA24><fA43 i1="01"><s1>INIST</s1><s2>18287</s2><s5>354000061890970006</s5></fA43><fA44><s0>9000</s0><s1>© 1997 Elsevier Science B.V. All rights reserved.</s1></fA44><fA47 i1="01" i2="1"><s0>97-0348288</s0></fA47><fA60><s1>P</s1></fA60><fA61><s0>A</s0></fA61><fA64 i1="01" i2="1"><s0>Discrete applied mathematics</s0></fA64><fA66 i1="01"><s0>NLD</s0></fA66><fC01 i1="01" l="ENG"><s0>Copyright (c) 1997 Elsevier Science B.V. All rights reserved. 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. 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