Why it matters

Edmonds' algorithm is matching classic. Understanding shapes theory.

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The architecture

Grow alternating tree from unmatched vertex.

Detect blossom (odd cycle).

Contract + continue.

Edmonds' blossomAlternating treegrow from unmatchedDetect blossomodd cycleContract + augmentexpand laterComplex bookkeeping; LEMON + networkx implement
Edmonds' blossom.
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How it works end to end

Edmonds 1965 landmark.

O(V^3) with careful impl.

Weighted case: Kuhn's for bipartite; more complex general.