Abstract:A classic theorem of Erdős and Pósa (1965) states that every graph has either k vertex-disjoint cycles or a set of O(k log k) vertices meeting all its cycles. While the standard proof revolves around finding a large 'frame' in the graph (a subdivision of a large cubic graph), an alternative way of proving this theorem is to use a ball packing argument of Kühn and Osthus (2003) and Diestel and Rempel (2005). In this paper, we argue that the latter approach is particularly well suited for studying edge variants … Show more
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