{"paper":{"title":"On resilience of connectivity in the evolution of random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luc Haller, Milo\\v{s} Truji\\'c","submitted_at":"2018-05-22T17:08:36Z","abstract_excerpt":"In this note we establish a resilience version of the classical hitting time result of Bollob\\'{a}s and Thomason regarding connectivity. A graph $G$ is said to be $\\alpha$-resilient with respect to a monotone increasing graph property $\\mathcal{P}$ if for every spanning subgraph $H \\subseteq G$ satisfying $\\mathrm{deg}_H(v) \\leq \\alpha \\cdot \\mathrm{deg}_G(v)$ for all $v \\in V(G)$, the graph $G - H$ still possesses $\\mathcal{P}$. Let $\\{G_i\\}$ be the random graph process, that is a process where, starting with an empty graph on $n$ vertices $G_0$, in each step $i \\geq 1$ an edge $e$ is chosen "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08744","kind":"arxiv","version":2},"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"}