## Electronic edition available at: http://www.math.uni-hamburg.de/home/diestel/books/graph.theory

- R. Diestel
- Graph Theory (3rd edition). Springer-Verlag,
- 2005

1 Excerpt

- Published 2008

Given an assignment of weights w to the edges of an infinite graph G, a matching M in G is called strongly w-maximal if for any matching N there holds ∑ {w(e) | e ∈ N \ M} ≤ ∑ {w(e) | e ∈ M \ N}. We prove that if w assumes only finitely many values all of which are rational then G has a strongly w-maximal matching. This result is best possible in the sense that if we allow irrational values or infinitely many values then there need not be a strongly w-maximal matching.

@inproceedings{Aharoni2008StronglyMM,
title={Strongly maximal matchings in infinite weighted graphs},
author={Ron Aharoni and Eli Berger and Agelos Georgakopoulos and Philipp Spr{\"{u}ssel},
year={2008}
}