Short Proofs of the Kneser-Lovász Coloring Principle
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- Aisenberg J., Bonet M.L., Buss S., Crãciun A., Istrate G. (2015) Short Proofs of the Kneser-Lovász Coloring Principle. In: Halldórsson M., Iwama K., Kobayashi N., Speckmann B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science, vol 9135. Springer, Berlin, Heidelberg
We prove that the propositional translations of the Kneser-Lovász theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lovász theorem that avoids the topological arguments of prior proofs for all but finitely many cases for each k. We introduce a miniaturization of the octahedral Tucker lemma, called the truncated Tucker lemma: it is open whether its propositional translations have (quasi-)polynomial size Frege or extended Frege proofs.
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