{"paper":{"title":"On the resilience of Hamiltonicity and optimal packing of Hamilton cycles in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Michael Krivelevich, Sonny Ben-Shimon","submitted_at":"2011-01-16T23:10:17Z","abstract_excerpt":"Let $\\bk=(k_1,...,k_n)$ be a sequence of $n$ integers. For an increasing monotone graph property $\\mP$ we say that a base graph $G=([n],E)$ is \\emph{$\\bk$-resilient} with respect to $\\mP$ if for every subgraph $H\\subseteq G$ such that $d_H(i)\\leq k_i$ for every $1\\leq i\\leq n$ the graph $G-H$ possesses $\\mP$. This notion naturally extends the idea of the \\emph{local resilience} of graphs recently initiated by Sudakov and Vu. In this paper we study the $\\bk$-resilience of a typical graph from $\\GNP$ with respect to the Hamiltonicity property where we let $p$ range over all values for which the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3099","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"}