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The thickness and chromatic number of r-inflated graphs

2010
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Discrete Mathematics
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Dedicated to Carsten Thomassen on the occasion of his 60th birthday. Abstract A graph has thickness t if the edges can be decomposed into t and no fewer planar layers. We study one aspect of a generalization of Ringel's famous Earth-Moon problem: what is the largest chromatic number of any thickness-2 graph? In particular, given a graph G we consider the r-inflation of G and find bounds on both the thickness and the chromatic number of the inflated graphs. In some instances the best possible

doi:10.1016/j.disc.2010.04.019
fatcat:nwylep7wfjfhvgb3yjia3lhhge