{"paper":{"title":"A Simple Extension of Dirac's Theorem on Hamiltonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Didem G\\\"oz\\\"upek, Mordechai Shalom, Sibel \\\"Ozkan, Yasemin B\\\"uy\\\"uk\\c{c}olak","submitted_at":"2016-06-12T09:16:51Z","abstract_excerpt":"The classical Dirac theorem asserts that every graph $G$ on $n$ vertices with minimum degree $\\delta(G) \\ge \\lceil n/2 \\rceil$ is Hamiltonian. The lower bound of $\\lceil n/2 \\rceil$ on the minimum degree of a graph is tight. In this paper, we extend the classical Dirac theorem to the case where $\\delta(G) \\ge \\lfloor n/2 \\rfloor $ by identifying the only non-Hamiltonian graph families in this case. We first present a short and simple proof. We then provide an alternative proof that is constructive and self-contained. Consequently, we provide a polynomial-time algorithm that constructs a Hamilt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03687","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"}