2026-04-19T11:33:53Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/1242742026-01-24T03:31:20Zcom_2072_1033col_2072_452950

00925njm 22002777a 4500 dc Aisenberg, James author Bonet Carbonell, M. Luisa author Buss, Sam author Craciun, Adrian author Istrate, Gabriel author 2018-08 We prove that propositional translations of the Kneser–Lovász theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs for all fixed values of k. We present a new counting-based combinatorial proof of the K neser–Lovász theorem based on the Hilton–Milner theorem; this avoids the topological arguments of prior proofs for all but finitely many base cases. We introduce new “truncated Tucker lemma” principles, which are miniaturizations of the octahedral Tucker lemma. The truncated Tucker lemma implies the Kneser–Lovász theorem. We show that the k=1 case of the truncated Tucker lemma has polynomial size extended Frege proofs. Peer Reviewed Postprint (author's final draft) Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica Polynomials Combinatorial proof Frege proofs Polynomial size Quasi-poly-nomial Kneser–Lovász theorem Hilton–Milner theorem Polinomis Short proofs of the Kneser-Lovász coloring principle