Short Proofs of the Kneser-Lovász Coloring Principle
نویسندگان
چکیده
We prove that the propositional translations of the KneserLovász theorem have polynomial size extended Frege proofs and quasipolynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lovász theorem that avoids the topological arguments of prior proofs. We introduce a miniaturization of the octahedral Tucker lemma, called the truncated Tucker lemma. The propositional translations of the truncated Tucker lemma are polynomial size and they imply the Kneser-Lovász principles with polynomial size Frege proofs. It is open whether they have (quasi-)polynomial size Frege or extended Frege proofs.
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