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Excluding any graph as a minor allows a low tree-width 2-coloring. (English) Zbl 1042.05036
Summary: 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.

##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C55 Generalized Ramsey theory 05C83 Graph minors
##### Keywords:
Tree-width; Vertex partitions; Edge partitions; Small components
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##### References:
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