On the Resolution Complexity of Graph Non-isomorphism

  • Jacobo Torán
Conference paper

DOI: 10.1007/978-3-642-39071-5_6

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7962)
Cite this paper as:
Torán J. (2013) On the Resolution Complexity of Graph Non-isomorphism. In: Järvisalo M., Van Gelder A. (eds) Theory and Applications of Satisfiability Testing – SAT 2013. SAT 2013. Lecture Notes in Computer Science, vol 7962. Springer, Berlin, Heidelberg

Abstract

For a pair of given graphs we encode the isomorphism principle in the natural way as a CNF formula of polynomial size in the number of vertices, which is satisfiable if and only if the graphs are isomorphic. Using the CFI graphs from [12], we can transform any undirected graph G into a pair of non-isomorphic graphs. We prove that the resolution width of any refutation of the formula stating that these graphs are isomorphic has a lower bound related to the expansion properties of G. Using this fact, we provide an explicit family of non-isomorphic graph pairs for which any resolution refutation requires an exponential number of clauses in the size of the initial formula. These graphs pairs are colored with color multiplicity bounded by 4. In contrast we show that when the color classes are restricted to have size 3 or less, the non-isomorphism formulas have tree-like resolution refutations of polynomial size.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jacobo Torán
    • 1
  1. 1.Institut für Theoretische InformatikUniversität UlmUlmGermany

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