{"paper":{"title":"A class of perfectly contractile graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fr\\'ed\\'eric Maffray, Nicolas Trotignon","submitted_at":"2013-09-02T15:25:00Z","abstract_excerpt":"We consider the class ${\\cal A}$ of graphs that contain no odd hole, no antihole, and no \"prism\" (a graph consisting of two disjoint triangles with three disjoint paths between them). We prove that every graph $G\\in{\\cal A}$ different from a clique has an \"even pair\" (two vertices that are not joined by a chordless path of odd length), as conjectured by Everett and Reed [see the chapter \"Even pairs\" in the book {\\it Perfect Graphs}, J.L. Ram\\'{\\i}rez-Alfons\\'{\\i}n and B.A. Reed, eds., Wiley Interscience, 2001]. Our proof is a polynomial-time algorithm that produces an even pair with the additi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0438","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}