#### Rank connectivity and pivot-minors of graphs

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dc.contributor.authorOum, Sang-ilko
dc.date.accessioned2023-01-09T02:00:09Z-
dc.date.available2023-01-09T02:00:09Z-
dc.date.created2023-01-09-
dc.date.issued2023-02-
dc.identifier.citationEUROPEAN JOURNAL OF COMBINATORICS, v.108-
dc.identifier.issn0195-6698-
dc.identifier.urihttp://hdl.handle.net/10203/304135-
dc.description.abstractThe cut-rank of a set X in a graph G is the rank of the X x (V(G) - X) submatrix of the adjacency matrix over the binary field. A split is a partition of the vertex set into two sets (X, Y) such that the cut-rank of X is less than 2 and both X and Y have at least two vertices. A graph is prime (with respect to the split decomposition) if it is connected and has no splits. A graph G is k+l-rank-connected if for every set X of vertices with the cut-rank less than k, |X| or |V(G) - X| is less than k + l. We prove that every prime 3+2-rank-connected graph G with at least 10 vertices has a prime 3+3-rank-connected pivot-minor H such that |V(H)| = |V(G)| - 1. As a corollary, we show that every excluded pivot-minor for the class of graphs of rank-width at most k has at most (3.5 middot 6k - 1)/5 vertices for k &gt;= 2. We also show that the excluded pivot-minors for the class of graphs of rank-width at most 2 have at most 16 vertices.(c) 2022 Elsevier Ltd. All rights reserved.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD-
dc.titleRank connectivity and pivot-minors of graphs-
dc.typeArticle-
dc.identifier.wosid000896749600001-
dc.identifier.scopusid2-s2.0-85141968083-
dc.type.rimsART-
dc.citation.volume108-
dc.citation.publicationnameEUROPEAN JOURNAL OF COMBINATORICS-
dc.identifier.doi10.1016/j.ejc.2022.103634-
dc.contributor.localauthorOum, Sang-il-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordPlusTHEOREM-
dc.subject.keywordPlusDECOMPOSITION-
dc.subject.keywordPlusWIDTH-
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