Excluding any graph as a minor allows a low tree-width 2-coloring
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-width at most k. Some generalizations are also proved. © 2003 Elsevier Inc. All rights reserved.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory. Series B
DeVos, M., Ding, G., Oporowski, B., Sanders, D., Reed, B., Seymour, P., & Vertigan, D. (2004). Excluding any graph as a minor allows a low tree-width 2-coloring. Journal of Combinatorial Theory. Series B, 91 (1), 25-41. https://doi.org/10.1016/j.jctb.2003.09.001