{"paper":{"title":"Packing Hamilton Cycles Online","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Frieze, Benny Sudakov, Joseph Briggs, Michael Krivelevich, Po-Shen Loh","submitted_at":"2016-08-17T14:28:26Z","abstract_excerpt":"It is known that w.h.p. the hitting time $\\tau_{2\\sigma}$ for the random graph process to have minimum degree $2\\sigma$ coincides with the hitting time for $\\sigma$ edge disjoint Hamilton cycles. In this paper we prove an online version of this property. We show that, for a fixed integer $\\sigma\\geq 2$, if random edges of $K_n$ are presented one by one then w.h.p. it is possible to color the edges online with $\\sigma$ colors so that at time $\\tau_{2\\sigma}$, each color class is Hamiltonian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04976","kind":"arxiv","version":5},"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"}