{"paper":{"title":"On Hamilton cycles in Erd\\H{o}s-R\\'{e}nyi subgraphs of large graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tony Johansson","submitted_at":"2018-11-08T15:43:19Z","abstract_excerpt":"Given a graph $\\Gamma = (V, E)$ on $n$ vertices and $m$ edges, we define the Erd\\H{o}s-R\\'{e}nyi graph process with host $\\Gamma$ as follows. A permutation $e_1,\\dots,e_m$ of $E$ is chosen uniformly at random, and for $t\\leq m$ we let $\\Gamma_t = (V, \\{e_1,\\dots,e_t\\})$. Suppose the minimum degree of $\\Gamma$ is $\\delta(\\Gamma) \\geq (1/2 + \\varepsilon)n$ for some constant $\\varepsilon > 0$. Then with high probability, $\\Gamma_t$ becomes Hamiltonian at the same moment that its minimum degree becomes at least two.\n  Given $0\\leq p\\leq 1$ we let $\\Gamma_p$ be the Erd\\H{o}s-R\\'{e}nyi subgraph of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03501","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"}