A weak form of Hadwiger's conjecture
classification
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keywords
kappaconjecturehadwigerweakcardinalchromaticcoloringfollowing
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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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