Ka,k minors in graphs of bounded tree-width

Authors:
Thomas Böhme;John Maharry;Bojan Mohar
Affiliations:
Institut für Mathematik, Technische Universität Ilmenau, Ilmenau, Germany;Department of Mathematics, The Ohio State University, Columbus, Ohio;Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia
Venue:
Journal of Combinatorial Theory Series B
Year:
2002

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Abstract

It is shown that for any positive integers k and w there exists a constant N = N(k,w) such that every 7-connected graph of tree-width less than w and of order at least N contains K3,k as a minor. Similar result is proved for Ka,k minors where a is an arbitrary fixed integer and the required connectivity depends only on a. These are the first results of this type where fixed connectivity forces arbitrarily large (nontrivial) minors.