{"paper":{"title":"Three Graphs and the Erd\\H{o}s-Gy\\'{a}rf\\'{a}s Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geoffrey Exoo","submitted_at":"2014-03-22T09:39:09Z","abstract_excerpt":"Three graphs related to the \\EGC\\, are presented. The graphs are derived from the Buckyball, the Petersen graph, and the Tutte-Coxeter graph. The first graph is a partial answer to a question posed by Heckman and Krakovski \\cite{planar} in their recent work on the planar version of the conjecture. The other two graphs appear to be the smallest known cubic graphs with no $2^m$-cycles for $m \\leq 4$ and for $m \\leq 5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5636","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"}