{"paper":{"title":"The number of edges of the edge polytope of a finite simple graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Shikama, Aki Mori, Hidefumi Ohsugi, Takayuki Hibi","submitted_at":"2013-08-16T01:01:39Z","abstract_excerpt":"Let $d \\geq 3$ be an integer. It is known that the number of edges of the edge polytope of the complete graph with $d$ vertices is $d(d-1)(d-2)/2$. In this paper, we study the maximum possible number $\\mu_d$ of edges of the edge polytope arising from finite simple graphs with $d$ vertices. We show that $\\mu_{d}=d(d-1)(d-2)/2$ if and only if $3 \\leq d \\leq 14$. In addition, we study the asymptotic behavior of $\\mu_d$. Tran--Ziegler gave a lower bound for $\\mu_d$ by constructing a random graph. We succeeded in improving this bound by constructing both a non-random graph and a random graph whose "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3530","kind":"arxiv","version":4},"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"}