Short Proofs of the Kneser-Lovász Coloring Principle

  • James Aisenberg
  • Maria Luisa Bonet
  • Sam Buss
  • Adrian Crãciun
  • Gabriel Istrate
Conference paper

DOI: 10.1007/978-3-662-47666-6_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9135)
Cite this paper as:
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

Abstract

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • James Aisenberg
    • 1
  • Maria Luisa Bonet
    • 2
  • Sam Buss
    • 1
  • Adrian Crãciun
    • 3
  • Gabriel Istrate
    • 3
  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA
  2. 2.Computer Science DepartmentUniversidad Politécnica de CataluñaBarcelonaSpain
  3. 3.West University of Timişoara, and the e-Austria Research InstituteTimişoaraRomania

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