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A weak form of Hadwiger's conjecture

Published 10 Dec 2013 in math.CO | (1312.2829v3)

Abstract: We introduce the following weak version of Hadwiger's conjecture: If $G$ is a graph and $\kappa$ is a cardinal such that there is no coloring map $c:G \to \kappa$, then $K_\kappa$ is a minor of $G$. We prove that this statement is true for graphs with infinite chromatic number

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