DC Field | Value | Language |
---|---|---|
dc.contributor.author | Dabrowski, Konrad K. | ko |
dc.contributor.author | Dross, Francois | ko |
dc.contributor.author | Jeong, Jisu | ko |
dc.contributor.author | Kante, Mamadou M. | ko |
dc.contributor.author | Kwon, O-joung | ko |
dc.contributor.author | Oum, Sang-il | ko |
dc.contributor.author | Paulusma, Daniel | ko |
dc.date.accessioned | 2021-12-27T06:40:14Z | - |
dc.date.available | 2021-12-27T06:40:14Z | - |
dc.date.created | 2021-12-24 | - |
dc.date.created | 2021-12-24 | - |
dc.date.created | 2021-12-24 | - |
dc.date.issued | 2021-12 | - |
dc.identifier.citation | SIAM JOURNAL ON DISCRETE MATHEMATICS, v.35, no.4, pp.2922 - 2945 | - |
dc.identifier.issn | 0895-4801 | - |
dc.identifier.uri | http://hdl.handle.net/10203/291328 | - |
dc.description.abstract | Tree-width and its linear variant path-width play a central role for the graph minor relation. In particular, Robertson and Seymour [J. Combin. Theory Ser. B, 35 (1983), pp. 39--61] proved that for every tree T, the class of graphs that do not contain T as a minor has bounded path width. For the pivot-minor relation, rank-width and linear rank-width take over the role of tree-width and path-width. As such, it is natural to examine if, for every tree T, the class of graphs that do not contain T as a pivot-minor has bounded linear rank-width. We first prove that this statement is false whenever T is a tree that is not a caterpillar. We conjecture that the statement is true if T is a caterpillar. We are also able to give partial confirmation of this conjecture by proving for every tree T, the class of T-pivot-minor-free distance-hereditary graphs has bounded linear rank-width if and only if T is a caterpillar; for every caterpillar T on at most four vertices, the class of T-pivot-minor-free graphs has bounded linear rank-width. To prove our second result, we only need to consider T = P-4 and T = K-1,K-3, but we follow a general strategy: first we show that the class of T-pivot-minor-free graphs is contained in some class of (H-1, H-2)-free graphs, which we then show to have bounded linear rank-width. In particular, we prove that the class of (K-3, S-1,S-2,S-2)-free graphs has bounded linear rank-width, which strengthens a known result that this graph class has bounded rank-width. | - |
dc.language | English | - |
dc.publisher | SIAM PUBLICATIONS | - |
dc.title | Tree Pivot-Minors and Linear Rank-Width | - |
dc.type | Article | - |
dc.identifier.wosid | 000736744500026 | - |
dc.identifier.scopusid | 2-s2.0-85073343795 | - |
dc.type.rims | ART | - |
dc.citation.volume | 35 | - |
dc.citation.issue | 4 | - |
dc.citation.beginningpage | 2922 | - |
dc.citation.endingpage | 2945 | - |
dc.citation.publicationname | SIAM JOURNAL ON DISCRETE MATHEMATICS | - |
dc.identifier.doi | 10.1137/21m1402339 | - |
dc.contributor.localauthor | Oum, Sang-il | - |
dc.contributor.nonIdAuthor | Dabrowski, Konrad K. | - |
dc.contributor.nonIdAuthor | Dross, Francois | - |
dc.contributor.nonIdAuthor | Jeong, Jisu | - |
dc.contributor.nonIdAuthor | Kante, Mamadou M. | - |
dc.contributor.nonIdAuthor | Kwon, O-joung | - |
dc.contributor.nonIdAuthor | Paulusma, Daniel | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | treepivot-minorlinear rank-width | - |
dc.subject.keywordPlus | CLIQUE-WIDTHGRAPH MINORSPARTITIONING PROBLEMSBIPARTITE GRAPHSCIRCLE GRAPH | - |
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