{"paper":{"title":"On covering expander graphs by Hamilton cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Krivelevich, Roman Glebov, Tibor Szab\\'o","submitted_at":"2011-11-14T19:06:14Z","abstract_excerpt":"The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum degree $\\Delta$ satisfies some basic expansion properties and contains a family of $(1-o(1))\\Delta/2$ edge disjoint Hamilton cycles, then there also exists a covering of its edges by $(1+o(1))\\Delta/2$ Hamilton cycles. This implies that for every $\\alpha >0$ and every $p \\geq n^{\\alpha-1}$ there exists a covering of all edges of $G(n,p)$ by $(1+o(1))np/2$ Hami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3325","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"}