{"paper":{"title":"A Size Condition for Diameter Two Orientable Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"\\'Eva Czabarka, Garner Cochran, L\\'aszl\\'o Sz\\'ekely, Peter Dankelmann","submitted_at":"2018-08-27T19:03:00Z","abstract_excerpt":"It was conjectured by Koh and Tay [Graphs Combin. 18(4) (2002), 745--756] that for $n\\geq 5$ every simple graph of order $n$ and size at least $\\binom{n}{2}-n+5$ has an orientation of diameter two. We prove this conjecture and hence determine for every $n\\geq 5$ the minimum value of $m$ such that every graph of order $n$ and size $m$ has an orientation of diameter two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08996","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"}