SWhat changed
Makes the odd-component deletion obstruction necessary and sufficient for perfect matching across the defined finite graph class, linked to the symbolic Pfaffian representation.
Scientific scope
Makes the odd-component deletion obstruction necessary and sufficient for perfect matching across the defined finite graph class, linked to the symbolic Pfaffian representation. The exact target is Theorem IV and the 109 Pfaffian lemma for the finite simplicial 1-complex graph class defined on 107, corresponding to finite simple undirected graphs. A factor means a spanning degree-one subgraph, or perfect matching. The condition is for every vertex subset, with odd-order components counted after deleting the subset and incident edges; one failed subset certifies nonexistence. Odd graph order is handled by the empty subset. The Pfaffian vanishing statement is symbolic over independent edge indeterminates, not an arbitrary numerical substitution test. This is not an efficient matching algorithm, randomized identity test or proof for infinite, directed, weighted or hypergraph matching. The paper's regular-graph application has extra hypotheses and is not an unconditional assertion about all regular graphs. No independent reconstruction, formal verification or performance measurement is recorded. Adjacent Taylor-series material on the shared first page and later Edmonds/general-factor extensions are excluded.
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
- William T. Tutte · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- W. T. Tutte, The Factorization of Linear Graphs, JLMS 22(1947),107–111; Michigan-hosted facsimile
- London Mathematical Society/Wiley metadata for Tutte's 1947 Factorization of Linear Graphs
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
Full scientific record · Browse contribution grades · Request a correction