Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
The authors prove (using transversal theory) infinite versions of the result due to P. D. Seymour (minimal non-two-colorable hypergraph on n vertices has at least n edges) and an unpublished result of M. Tarsi. They give a characterization of the structure of minimal unsatisfiable CNF formulas in n variables containing exactly \(n+1\) clauses and its geometrical interpretation.
scientific article; zbMATH DE number 3987323