{"paper":{"title":"On $k$-ordered Hamiltonian Graphs","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gabor N. Sarkozy, Stanley Selkow","submitted_at":"1996-12-04T00:00:00Z","abstract_excerpt":"A Hamiltonian graph $G$ of order $n$ is $k$-ordered, $2\\leq k \\leq n$, if for every sequence $v_1, v_2, \\ldots ,v_k$ of $k$ distinct vertices of $G$, there exists a Hamiltonian cycle that encounters $v_1, v_2, \\ldots , v_k$ in this order. In this paper, answering a question of Ng and Schultz, we give a sharp bound for the minimum degree guaranteeing that a graph is a $k$-ordered Hamiltonian graph under some mild restrictions. More precisely, we show that there are $\\varepsilon, n_0> 0$ such that if $G$ is a graph of order $n\\geq n_0$ with minimum degree at least $\\lceil \\frac{n}{2} \\rceil + \\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9612212","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"}