Countable Menger's theorem with finitary matroid constraints on the ingoing edges

Joó, Attila (2018) Countable Menger's theorem with finitary matroid constraints on the ingoing edges. ELECTRONIC JOURNAL OF COMBINATORICS, 25 (3). ISSN 1097-1440

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Abstract

We present a strengthening of the countable Menger's theorem of R. Aharoni. Let D = (V, A) be a countable digraph with s not equal t is an element of V and let M = O-v is an element of v M(v )be a matroid on A where M-v is a finitary matroid on the ingoing edges of v. We show that there is a system of edge-disjoint s -> t paths P such that the united edge set of these paths is M-independent, and there is a C not subset of A consisting of one edge from each element of P for which span(M)(C) covers all the s -> t paths in D.

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