##### Short Proofs of the Kneser-Lovász Coloring Principle

We prove that the propositional translations of the Kneser-Lovasz theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lovasz 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

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