Title:
Excluded Forest Minors and the Erdos-Posa Property
Excluded Forest Minors and the Erdos-Posa Property
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Joret, Gwenael
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Abstract
A classical result of Robertson and Seymour states that the set of graphs containing a fixed planar graph H as a minor has the so-called Erdos-Posa property; namely, there exists a function f depending only on H such that, for every graph G and every positive integer k, either G has k vertex-disjoint subgraphs each containing H as a minor, or there exists a subset X of vertices of G of size at most f(k) such that G - X has no H-minor. While the best function f currently known is super-exponential in k, a O(k \log k) bound is known in the special case where H is a forest. This is a consequence of a theorem of Bienstock, Robertson, Seymour, and Thomas on the pathwidth of graphs with an excluded forest-minor. In this talk I will sketch a proof that the function f can be taken to be linear when H is a forest. This is best possible in the sense that no linear bound exists if H has a cycle. Joint work with S. Fiorini and D. R. Wood.
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NSF, NSA, ONR, IMA, Colleges of Sciences, Computing and Engineering
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2012-05
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Proceedings