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dc.contributor.authorChudnovsky, Maria
dc.contributor.authorScott, Alex
dc.contributor.authorSeymour, Paul
dc.contributor.authorSpirkl, Sophie 16:27:45 (GMT) 16:27:45 (GMT)
dc.descriptionThis publication is available at Elsevier via © 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC-BY license (
dc.description.abstractA theorem of Mader shows that every graph with average degree at least eight has a K6 minor, and this is false if we replace eight by any smaller constant. Replacing average degree by minimum degree seems to make little difference: we do not know whether all graphs with minimum degree at least seven have K6 minors, but minimum degree six is certainly not enough. For every ε > 0 there are arbitrarily large graphs with average degree at least 8 − ε and minimum degree at least six, with no K6 minor. But what if we restrict ourselves to bipartite graphs? The first statement remains true: for every ε > 0 there are arbitrarily large bipartite graphs with average degree at least 8 − ε and no K6 minor. But surprisingly, going to minimum degree now makes a significant difference. We will show that every bipartite graph with minimum degree at least six has a K6 minor. Indeed, it is enough that every vertex in the larger part of the bipartition has degree at least six.en
dc.description.sponsorshipNSF DMS-EPSRC, DMS-2120644 || EPSRC, EP/V007327/1 || NSF, DMS-2154169 || AFOSR, A9550-19-1-0187 || NSERC, RGPIN-2020-03912.en
dc.relation.ispartofseriesJournal of Combinatorial Theory, Series B;
dc.rightsAttribution 4.0 International*
dc.titleBipartite graphs with no K6 minoren
dcterms.bibliographicCitationChudnovsky, M., Scott, A., Seymour, P., & Spirkl, S. (2024a). Bipartite graphs with no K6 minor. Journal of Combinatorial Theory, Series B, 164, 68–104.
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Combinatorics and Optimizationen

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