{"paper":{"title":"Deciding Graph non-Hamiltonicity via a Closure Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"A. Lee, C. E. Bell, E. R. Swart, N. R. Swart, S. J. Gismondi","submitted_at":"2016-11-05T23:38:23Z","abstract_excerpt":"We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the $n!$ Hamilton cycles in a complete directed graph on $n+1$ vertices corresponds with each of the $n!$ $n$-permutation matrices $P$, such that $p_{u,i}=1$ if and only if the $i^{th}$ arc in a cycle enters vertex $u$, starting and ending at vertex $n+1$. A graph instance ($G$) is initially coded as exclusion set $E$, whose members are pairs of components of $P$, $\\{p_{u,i} ,p_{v,i+1}\\}, i=1,n-1$, for each arc $(u,v)$ not in $G$. For each $\\{p_{u,i} ,p_{v,i+1}\\}\\in E$, the set of $P$ satisfyin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01710","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"}