The Erdös-Pósa property for clique minors in highly connected graphs

Details The Erdös-Pósa property for clique minors in highly connected graphs The Erdös-Pósa property for clique minors in highly connected graphs

2010-03-20

arxiv.org/abs/1003.3915v1

Mathematics

Combinatorics

Scientific paper

We prove the existence of a function f: N^2 -> N such that for all p,k in N every (k(p-3) + 14p+14) - connected graph either has k disjoint K_p minors or contains a set of at most f(p,k) vertices whose deletion kills all its K_p minors. For fixed p > 4, the connectivity bound of about k(p-3) is smallest possible, up to an additive constant: if we assume less connectivity in terms of k, there will be no such function f.

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