Let H=(V,E) be a hypergraph and let k \ge 1 and l \ge 0 be fixed integers. Let M be the matroid with ground-set E s.t. a set F \subseteq E is independent if and only if each X \subseteq V with k|X|-l \ge 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 Lovász' min-max formula on the maximum matroid matching holds for M. Our result implies the Berge-Tutte formula on the maximum matching of graphs (k=1, l=0), generalizes Lovász' graphic matroid (cycle matroid) matching formula to hypergraphs (k=l=1) and gives a min-max formula for the maximum matroid matching in the 2-dimensional rigidity matroid (k=2, l=3).
Bibtex entry:
@techreport{egres-05-11,
AUTHOR | = | {Makai, M{\'a}rton}, |
TITLE | = | {Matroid matching with Dilworth truncation}, |
NOTE | = | {{\tt www.cs.elte.hu/egres}}, |
INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
YEAR | = | {2005}, |
NUMBER | = | {TR-2005-11} |