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arXiv · 1505.05531

Short Proofs of the Kneser-Lov\'asz Coloring Principle

James Aisenberg·Maria Luisa Bonet·Sam Buss·Adrian Crãciun·Gabriel Istrate
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Abstract

We prove that the propositional translations of the Kneser-Lov\'asz theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs. We present a new counting-based combinatorial proof of the Kneser-Lov\'asz 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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James Aisenberg, Maria Luisa Bonet, Sam Buss, Adrian Crãciun, Gabriel Istrate. 2015-05-20. Short Proofs of the Kneser-Lov\'asz Coloring Principle. https://arxiv.org/abs/1505.05531

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