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EnglishWe 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.
| Titolo: | Set Graphs. III. Proof Pearl: Claw-Free Graphs Mirrored into Transitive Hereditarily Finite Sets |
| Autori: | |
| Data di pubblicazione: | 2012 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11368/2740501 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10817-012-9272-3 |
| URL: | http://link.springer.com/article/10.1007%2Fs10817-012-9272-3 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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