Tutte–Berge formula

In the mathematical discipline of graph theory the Tutte–Berge formula is a characterization of the size of a maximum matching in a graph. It is a generalization of Tutte's theorem on perfect matchings, and is named after W. T. Tutte (who proved Tutte's theorem) and Claude Berge (who proved its generalization).

The theorem states that the size of a maximum matching of a graph ${\displaystyle G=(V,E)}$ equals

where ${\displaystyle \operatorname {odd} (H)}$ counts how many of the connected components of the graph ${\displaystyle H}$ have an odd number of vertices.

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