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Set Graphs. III. Proof Pearl: Claw-Free Graphs Mirrored into Transitive Hereditarily Finite Sets

Journal of Automated Reasoning volume 52, pages 1–29 (2014)Cite this article

Abstract

We report on the formalization of two classical results about claw-free graphs, which have been verified correct by Jacob T. Schwartz’s proof-checker Referee. We have proved formally that every connected claw-free graph admits (1) a near-perfect matching, (2) Hamiltonian cycles in its square. To take advantage of the set-theoretic foundation of Referee, we exploited set equivalents of the graph-theoretic notions involved in our experiment: edge, source, square, etc. To ease some proofs, we have often resorted to weak counterparts of well-established notions such as cycle, claw-freeness, longest directed path, etc.

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Authors and Affiliations

  1. DiGe/DMI, Università di Trieste, Via Valerio, 12/1, 34127, Trieste, Italy

    Eugenio G. Omodeo

  2. DiMI, Università di Udine, Via delle Scienze, 206, 33100, Udine, Italy

    Alexandru I. Tomescu

  3. FMI, University of Bucharest, Str. Academiei, 14, 010014, Bucharest, Romania

    Alexandru I. Tomescu

Authors
  1. Eugenio G. Omodeo
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  2. Alexandru I. Tomescu
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Correspondence to Eugenio G. Omodeo.

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Omodeo, E.G., Tomescu, A.I. Set Graphs. III. Proof Pearl: Claw-Free Graphs Mirrored into Transitive Hereditarily Finite Sets. J Autom Reasoning 52, 1–29 (2014). https://doi.org/10.1007/s10817-012-9272-3

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  • DOI: https://doi.org/10.1007/s10817-012-9272-3

Keywords

  • Claw-free graph
  • Theory-based automated reasoning
  • Proof-checking
  • Referee