Matroid matching with Dilworth truncation

Let H = (V, E) be a hypergraph and let k >= 1 and l >= 0 be fixed integers. Let M be the matroid with ground-set E s.t. a set F subset of E is independent if and only if each X subset of V with k|X| - l >= 0 spans at most k |X| - l hyperedges of F. We prove that if H is dense enough, then M satisfies the double circuit property, thus Lovasz' min-max formula on the maximum matroid matching holds for Our result implies the Berge-Tutte formula on the maximum matching of graphs (k = 1, l = 0), generalizes Lovasz' graphic matroid (cycle matroid) matching formula to hypergraphs (k = l = 1) and gives a min-max formula for the maximum matroid matching in the two-dimensional rigidity matroid (k = 2, l = 3). (C) 2007 Published by Elsevier B.V.