{"paper":{"title":"A Distributed Algorithm for Finding Hamiltonian Cycles in Random Graphs in O(log n) Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Volker Turau","submitted_at":"2018-05-17T12:38:15Z","abstract_excerpt":"It is known for some time that a random graph $G(n,p)$ contains w.h.p. a Hamiltonian cycle if $p$ is larger than the critical value $p_{crit}= (\\log n + \\log \\log n + \\omega_n)/n$. The determination of a concrete Hamiltonian cycle is even for values much larger than $p_{crit}$ a nontrivial task. In this paper we consider random graphs $G(n,p)$ with $p$ in $\\tilde{\\Omega}(1/\\sqrt{n})$, where $\\tilde{\\Omega}$ hides poly-logarithmic factors in $n$. For this range of $p$ we present a distributed algorithm ${\\cal A}_{HC}$ that finds w.h.p. a Hamiltonian cycle in $O(\\log n)$ rounds. The algorithm wo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06728","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"}