Abstract
Counting maximum matchings in a graph is of great interest in statistical mechanics, solid-state chemistry, theoretical computer science, mathematics, among other disciplines. However, it is a challengeable problem to explicitly determine the number of maximum matchings of general graphs. In this paper, using Gallai–Edmonds structure theorem, we derive a computing formula for the number of maximum matchings in a graph. According to the formula, we obtain an algorithm to enumerate maximum matchings of a graph. In particular, the formula implies that computing the number of maximum matchings of a graph is converted to computing the number of perfect matchings of some induced subgraphs of the graph.
Published Version
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