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

Authors:
Eugenio G. Omodeo;Alexandru I. Tomescu
Affiliations:
DiGe/DMI, Università di Trieste, Trieste, Italy 34127;DiMI, Università di Udine, Udine, Italy 33100 and FMI, University of Bucharest, Bucharest, Romania 010014
Venue:
Journal of Automated Reasoning
Year:
2014

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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.