On provably disjoint NP-pairs

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Resolution Lower Bounds for Perfect Matching Principles

For an arbitrary hypergraph H, let PM(H) be the propositional formula asserting that contains a perfect matching. We show that every resolution refutation of PM(H) must have size #(H)r(H)(log n(H))(r(H) + log n(H)) where n(H) is the number of vertices, #(H) is the minimal degree of a vertex, r(H) is the maximal size of an edge, and #(H) is the maximal number of edges incident to two di#erent vertices