Abstract:Which graph classes C exclude a fixed ladder as a minor? We show that this is the case if and only if all graphs G in C admit a proper vertex coloring with a bounded number of colors such that for every 2-connected subgraph H of G, there is a color that appears exactly once in H. If one were considering all connected subgraphs of G instead, then such a coloring is known as a centered coloring, and the minimum achievable number of colors is the treedepth of G. Classes of graphs with bounded treedepth are exactl… Show more
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