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21st Cumberland Conference on Graph Theory, Combinatorics, and Computing ---In Honor of Mike Plummer's 70th Birthday
May 15-17, 2008
Vanderbilt University
Nashville, TN, USA

Organizers
Mark Ellingham and Gexin Yu

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A special case of Hadwiger's conjecture
by
Jonah Blasiak
University of California Berkeley

We present some partial results on Hadwiger's conjecture for graphs with no stable set of size 3. Such a graph on at least 2t-1 vertices is not t-1 colorable, so is conjectured to have a Kt minor. There is a strengthening of Hadwiger's conjecture in this case, which states that there is a Kt minor in which the preimage of each vertex of Kt is a single vertex or an edge. We prove this strengthened version for graphs with an even number of vertices and fractional clique covering number less than 3.

Date received: April 16, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawn-40.