A tight Erdős-Pósa function for wheel minors

10/17/2017

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by   Pierre Aboulker, et al.

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Let W_t denote the wheel on t+1 vertices. We prove that for every integer t ≥ 3 there is a constant c=c(t) such that for every integer k≥ 1 and every graph G, either G has k vertex-disjoint subgraphs each containing W_t as minor, or there is a subset X of at most c k k vertices such that G-X has no W_t minor. This is best possible, up to the value of c. We conjecture that the result remains true more generally if we replace W_t with any fixed planar graph H.