SWhat changed
A finite simple graph is perfect exactly when it has neither an induced odd cycle of length at least five nor the complement of such a cycle. A structural decomposition of Berge graphs, together with exclusions for a minimal imperfect graph, yields the characterization.
Scientific scope
A finite simple graph is perfect exactly when it has neither an induced odd cycle of length at least five nor the complement of such a cycle. A structural decomposition of Berge graphs, together with exclusions for a minimal imperfect graph, yields the characterization. Perfection concerns every induced subgraph, not only the original graph's chromatic and clique numbers. This contribution is the structural theorem, not automatically a new optimal recognition or coloring algorithm.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. Perfection concerns every induced subgraph, not only the original graph's chromatic and clique numbers. This contribution is the structural theorem, not automatically a new optimal recognition or coloring algorithm.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
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