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Hadwigers Conjecture for inflations of 3-chromatic graphs
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
University of Southern Denmark, Denmark; Aarhus University Hospital, Denmark.
2016 (English)In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 51, 99-108 p.Article in journal (Refereed) Published
Abstract [en]

Hadwigers Conjecture states that every k-chromatic graph has a complete minor of order k. A graph G is an inflation of a graph G if G is obtained from G by replacing each vertex upsilon of G by a clique C-upsilon and joining two vertices of distinct cliques by an edge if and only if the corresponding vertices of G are adjacent. We present an algorithm for computing an upper bound on the chromatic number chi (G) of any inflation G of any 3-chromatic graph G. As a consequence, we deduce that Hadwigers Conjecture holds for any inflation of any 3-colorable graph. (C) 2015 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
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Discrete Mathematics
URN: urn:nbn:se:liu:diva-122185DOI: 10.1016/j.ejc.2015.05.003ISI: 000362144400007OAI: diva2:865071

Funding Agencies|SVeFUM; Mittag-Leffler Institute

Available from: 2015-10-26 Created: 2015-10-23 Last updated: 2015-11-19

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Casselgren, Carl Johan
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