Excluding any graph as a minor allows a low tree-width 2-coloring

Authors:
Matt DeVos;Guoli Ding;Bogdan Oporowski;Daniel P. Sanders;Bruce Reed;Paul Seymour;Dirk Vertigan
Affiliations:
Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ;Department of Mathematics, Louisiana State University, Baton Rouge, LA;Department of Mathematics, Louisiana State University, Baton Rouge, LA;Equipe Combinatoire, Université Pierre et Marie Curie, Case 189, 4 place Jussieu, Paris 75252 Cedex 05, France;School of Computer Science, McGill University, 3480 University, Montreal, Quebec, Canada H3A 2A7;Mathematics Department & PACM, Princeton University, Fine Hall, Washington Road, Princeton, NJ;Department of Mathematics, Louisiana State University, Baton Rouge, LA
Venue:
Journal of Combinatorial Theory Series B
Year:
2004

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Abstract

This article proves the conjecture of Thomas that, for every graph G, there is an integer k such that every graph with no minor isomorphic to G has a 2-coloring of either its vertices or its edges where each color induces a graph of tree-widlh at most k. Some generalizations are also proved.