Rank-width and vertex-minors

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dc.contributor.authorOum, Sang-ilko
dc.date.accessioned2013-03-06T17:07:56Z-
dc.date.available2013-03-06T17:07:56Z-
dc.date.created2012-02-06-
dc.date.created2012-02-06-
dc.date.issued2005-09-
dc.identifier.citationJOURNAL OF COMBINATORIAL THEORY SERIES B, v.95, no.1, pp.79 - 100-
dc.identifier.issn0095-8956-
dc.identifier.urihttp://hdl.handle.net/10203/87720-
dc.description.abstractThe rank-width is a graph parameter related in terms of fixed functions to clique-width but more tractable. Clique-width has nice algorithmic properties, but no good "minor" relation is known analogous to graph minor embedding for tree-width. In this paper, we discuss the vertex-minor relation of graphs and its connection with rank-width. We prove a relationship between vertex-minors of bipartite graphs and minors of binary matroids, and as an application, we prove that bipartite graphs of sufficiently large rank-width contain certain bipartite graphs as vertex-minors. The main theorem of this paper is that for fixed k, there is a finite list of graphs such that a graph G has rank-width at most k if and only if no graph in the list is isomorphic to a vertex-minor of G. Furthermore, we prove that a graph has rank-width at most I if and only if it is distance-hereditary. (C) 2005 Elsevier Inc. All rights reserved.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.subjectGRAPH MINORS-
dc.subjectBRANCH-WIDTH-
dc.subjectPLANAR GRAPH-
dc.subjectCLIQUE-WIDTH-
dc.subjectMATROIDS-
dc.subjectDECOMPOSITION-
dc.subjectOBSTRUCTIONS-
dc.titleRank-width and vertex-minors-
dc.typeArticle-
dc.identifier.wosid000231264400006-
dc.identifier.scopusid2-s2.0-23244468510-
dc.type.rimsART-
dc.citation.volume95-
dc.citation.issue1-
dc.citation.beginningpage79-
dc.citation.endingpage100-
dc.citation.publicationnameJOURNAL OF COMBINATORIAL THEORY SERIES B-
dc.identifier.doi10.1016/j.jctb.2005.03.003-
dc.contributor.localauthorOum, Sang-il-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorclique-width-
dc.subject.keywordAuthorrank-width-
dc.subject.keywordAuthorvertex-minor-
dc.subject.keywordAuthorlocal complementation-
dc.subject.keywordAuthorpivoting-
dc.subject.keywordAuthorbranch-width-
dc.subject.keywordAuthorbinary matroid-
dc.subject.keywordPlusGRAPH MINORS-
dc.subject.keywordPlusBRANCH-WIDTH-
dc.subject.keywordPlusPLANAR GRAPH-
dc.subject.keywordPlusCLIQUE-WIDTH-
dc.subject.keywordPlusMATROIDS-
dc.subject.keywordPlusDECOMPOSITION-
dc.subject.keywordPlusOBSTRUCTIONS-
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