SWhat changed
Conditioned blossom contraction,alternating-tree search and expansion give a conceptual polynomial cardinality-matching method in general graphs, together with odd-set-cover duality.
Scientific scope
Conditioned blossom contraction,alternating-tree search and expansion give a conceptual polynomial cardinality-matching method in general graphs, together with odd-set-cover duality. Finite general graph, maximum cardinality rather than maximum weight or hypergraph matching. Original 450–452 gives a conceptual algorithm and n^4 time/n^2 memory upper bounds under its step/storage accounting; no modern tightbound or measured runtime is claimed. Safe maximality preservation uses a blossom belonging to a flower/stem; arbitrary odd-cycle contraction is not a universal equivalence. Retained pseudovertices may need expansion when inner vertices, as 465–466 explain. The odd-set-cover duality is proved here; the stronger full matching-polytope/weighted optimization proof is explicitly deferred to another paper and excluded from this target. Original discussion of polynomial efficiency is informal foundational reasoning, not a formal proof that every polynomial algorithm is practical or a solution of Pversus NP. no independent proof reconstruction, runnable implementation or benchmark certification. Berge, Norman/Rabin, Tutte, network-flow predecessors, Dantzig discussions and Witzgall’s proof suggestion remain distinct inputs.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Jack Edmonds · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Edmonds: Paths, Trees, and Flowers(1965), original 449–467
- Cambridge: Paths, Trees, and Flowers original 1965 publication metadata
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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