Strongly maximal matchings in infinite weighted graphs

Mathematics – Combinatorics

Scientific paper

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17 pages

Scientific paper

Given an assignment of weights w to the edges of a graph G, a matching M in G
is called strongly w-maximal if for any matching N the sum of weights of the
edges in N\M is at most the sum of weights of the edges in 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.

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