{"paper":{"title":"Oriented discrepancy of Hamilton cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lior Gishboliner, Michael Krivelevich, Peleg Michaeli","submitted_at":"2022-03-14T14:44:45Z","abstract_excerpt":"We propose the following conjecture extending Dirac's theorem: if $G$ is a graph with $n\\ge 3$ vertices and minimum degree $\\delta(G)\\ge n/2$, then in every orientation of $G$ there is a Hamilton cycle with at least $\\delta(G)$ edges oriented in the same direction. We prove an approximate version of this conjecture, showing that minimum degree $n/2 + O(k)$ guarantees a Hamilton cycle with at least $(n+k)/2$ edges oriented in the same direction. We also study the analogous problem for random graphs, showing that if the edge probability $p = p(n)$ is above the Hamiltonicity threshold, then, with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.07148","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.07148/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}