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A Unified Approach for Solving Vertex Partitioning Problems in Polynomial Time

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33 pages
Introduction and definitions Some results Conclusion A Unified Approach for Solving Vertex Partitioning Problems in Polynomial Time Remy Belmonte Martin Vatshelle Department of Informatics, University of Bergen, Norway 2nd Workshop on Graph Decompositions Theoretical, Algorithmic and Logical Aspects October 19, 2010 Remy Belmonte, Martin Vatshelle University of Bergen Solving Vertex Partitioning Problems 1/ 33

  • vertex partitioning

  • bergen solving

  • tolerance strongly

  • trivially perfect

  • perfect comparability

  • bounded tolerance

  • k?trapezoid circular

  • polynomial time


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Re´myBelmonteMartinVatshelleDepartmentofInformatics,UniversityofBergen,Norway2ndWorkshoponGraphDecompositionsTheoretical,AlgorithmicandLogicalAspectsOctober19,2010AUnifiedApproachforSolvingVertexPartitioningProblemsinPolynomialTime33/1smelborPgninoititraPxetreVgnivloSnegreBfoytisrevinUellehstaVnitraM,etnomleByme´RnoisulcnoCstluseremoSsnoitineddnanoitcudortnI
treVgnivloSnegreBfoytisrevinUellehstaVnitraM,etnomleByme´RFindinglargegraphclasseshavingboolean-widthO(logn).OurgoalBui-Xuan,TelleandVatshelle[’09]showedthatcertainvertexpartitioningproblemscanbesolvedinpolynomialtimeongraphshavingboolean-widthO(logn).Theseproblemsinclude:IndependentSet,DominatingSet,PerfectCode,k-Coloring,H-Cover,H-Homomorphism,MotivationnoisulcnoCstluseremoSsnoitineddnanoitcudortnI33/2smelborPgninoititraPxe
hparGe´RymeBmlnoetclasses,aMtrniaVstehlIntroductionanddefinitionsSomeresultsConclusionorderedelUybinevsrtiinclusionyfoeBgrneoSvlnigeVtrxeaPtrtioiingnrPboelsm/333