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

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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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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Keywords

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