Excluded vertex-minors for graphs of linear rank-width at most k

Cited 10 time in webofscience Cited 0 time in scopus
  • Hit : 400
  • Download : 0
DC FieldValueLanguage
dc.contributor.authorJeong, Jisuko
dc.contributor.authorKwon, O-Joungko
dc.contributor.authorOum, Sang-ilko
dc.date.accessioned2014-09-04T08:24:18Z-
dc.date.available2014-09-04T08:24:18Z-
dc.date.created2014-08-04-
dc.date.created2014-08-04-
dc.date.issued2014-10-
dc.identifier.citationEUROPEAN JOURNAL OF COMBINATORICS, v.41, pp.242 - 257-
dc.identifier.issn0195-6698-
dc.identifier.urihttp://hdl.handle.net/10203/189963-
dc.description.abstractLinear rank-width is a graph width parameter, which is a variation of rank-width by restricting its tree to a caterpillar. As a corollary of known theorems, for each k, there is a finite obstruction set O-k of graphs such that a graph G has linear rank-width at most k if and only if no vertex-minor of G is isomorphic to a graph in O-k However, no attempts have been made to bound the number of graphs in O-k for k >= 2. We show that for each k, there are at least 2(Omega(3k)) pairwise locally non-equivalent graphs in O-k, and therefore the number of graphs in O-k is at least double exponential. To prove this theorem, it is necessary to characterize when two graphs in O-k are locally equivalent. A graph is a block graph if all of its blocks are complete graphs. We prove that if two block graphs without simplicial vertices of degree at least 2 are locally equivalent, then they are isomorphic. This not only is useful for our theorem but also implies a theorem of Bouchet (1988) stating that if two trees are locally equivalent, then they are isomorphic.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD-
dc.subjectBRANCH-WIDTH-
dc.subjectOBSTRUCTIONS-
dc.titleExcluded vertex-minors for graphs of linear rank-width at most k-
dc.typeArticle-
dc.identifier.wosid000338399000017-
dc.identifier.scopusid2-s2.0-84900810518-
dc.type.rimsART-
dc.citation.volume41-
dc.citation.beginningpage242-
dc.citation.endingpage257-
dc.citation.publicationnameEUROPEAN JOURNAL OF COMBINATORICS-
dc.identifier.doi10.1016/j.ejc.2014.04.010-
dc.contributor.localauthorOum, Sang-il-
dc.type.journalArticleArticle-
dc.subject.keywordPlusBRANCH-WIDTH-
dc.subject.keywordPlusOBSTRUCTIONS-
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 10 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0