Blossom
Odd-length cycle detected during augmenting path search. Contract to single vertex, search continues.
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Complexity
O(V³) classical. O(E · V · α(V)) modern. Micali-Vazirani: O(E · √V) — extreme complexity, rarely implemented.
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Why odd cycles matter
Bipartite has no odd cycles → simple. Odd cycles enable extra matchings via blossoms.
Applications
Chinese postman on non-Eulerian. General matching problems in networks.