Abstract: |
A matching in a graph G is a subset M of the
edges of G such that no two share an endpoint. A matching has maximum
cardinality if its cardinality is at least as large as that of any other
matching. An odd-set cover OSC of a graph G is a
labeling of the nodes of G with integers such that every edge of
G is either incident to a node labeled 1 or connects two nodes
labeled with the same number i ≥ 2.
This article proves Edmonds theorem:
Let M be a matching in a graph G and let OSC be an
odd-set cover of G.
For any i ≥ 0, let n(i) be the number of nodes
labeled i. If |M| = n(1) +
∑i ≥ 2(n(i) div 2),
then M is a maximum cardinality matching.
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BibTeX: |
@article{Max-Card-Matching-AFP,
author = {Christine Rizkallah},
title = {Maximum Cardinality Matching},
journal = {Archive of Formal Proofs},
month = jul,
year = 2011,
note = {\url{http://isa-afp.org/entries/Max-Card-Matching.html},
Formal proof development},
ISSN = {2150-914x},
}
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