{"paper":{"title":"Compatible Hamilton cycles in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Choongbum Lee, Michael Krivelevich","submitted_at":"2014-10-06T16:16:01Z","abstract_excerpt":"A graph is Hamiltonian if it contains a cycle passing through every vertex. One of the cornerstone results in the theory of random graphs asserts that for edge probability $p \\gg \\frac{\\log n}{n}$, the random graph $G(n,p)$ is asymptotically almost surely Hamiltonian. We obtain the following strengthening of this result. Given a graph $G=(V,E)$, an {\\em incompatibility system} $\\mathcal{F}$ over $G$ is a family $\\mathcal{F}=\\{F_v\\}_{v\\in V}$ where for every $v\\in V$, the set $F_v$ is a set of unordered pairs $F_v \\subseteq \\{\\{e,e'\\}: e\\ne e'\\in E, e\\cap e'=\\{v\\}\\}$. An incompatibility system "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1438","kind":"arxiv","version":3},"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"}