Maximum Cardinality Matching

 Title: Maximum Cardinality Matching Author: Christine Rizkallah Submission date: 2011-07-21 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. 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}, } License: BSD License