Why it matters

General matching handles non-bipartite. Understanding shapes advanced algorithms.

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The architecture

Search for augmenting path.

Blossom: odd cycle contracts to single vertex.

Augment; expand.

Blossom algorithmAugmenting pathsearchBlossomodd cycle contractAugment + expandmatch updateEdmonds 1965; Micali-Vazirani 1980 improved to O(sqrt(V) E)
General matching.
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How it works end to end

Blossom = odd cycle in alternating tree.

Contract to virtual vertex.

Augmenting path found; expand blossoms.