Short Proofs of the Kneser-Lovász Coloring Principle

  • James Aisenberg
  • Maria Luisa Bonet
  • Sam Buss
  • Adrian Crãciun
  • Gabriel Istrate
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9135)


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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