2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 175180
author:  Márton Makai 

title:  Matroid matching with Dilworth truncation 
keywords:  matroid matching, Dilworth truncation, double circuit property 
abstract: 
Let
H=(V,E)
be a hypergraph and let
k≥1
and
l≥0
be fixed integers. Let
M
E
s.t. a set
F⊆E
is independent if and only if each
X⊆V
with
kXl≥0
spans at most
kXl
hyperedges of
F
. We prove that if
H
is dense enough, then
M
M
k=1
,
l=0
), generalizes Lovász' graphic matroid (cycle
matroid) matching formula to hypergraphs (
k=l=1
) and gives a minmax formula for the maximum matroid
matching in the 2dimensional rigidity matroid (
k=2
,
l=3
).

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reference:  Márton Makai (2005), Matroid matching with Dilworth truncation, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 175180 
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