Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas

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Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas

Seymour (Quart. J. Math. Oxford 25 (1974), 303-312) proved that a minimal non 2-colorable hypergraph on n vertices has at least n edges. A related fact is that a minimal unsatistiable CNF formula in n variables has at least n + 1 clauses (an unpublished result of M. Tarsi.) The link between the two results is shown; both are given infinite versions and proved using transversal theory (Seymour’s...

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ژورنال

عنوان ژورنال: Journal of Combinatorial Theory, Series A

سال: 1986

ISSN: 0097-3165

DOI: 10.1016/0097-3165(86)90060-9