{"paper":{"title":"The emergence of a giant component in random subgraphs of pseudo-random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Frieze, Michael Krivelevich, Ryan R. Martin","submitted_at":"2016-05-21T13:40:46Z","abstract_excerpt":"Let $G$ be a $d$-regular graph $G$ on $n$ vertices. Suppose that the adjacency matrix of $G$ is such that the eigenvalue $\\lambda$ which is second largest in absolute value satisfies $\\lambda=o(d)$. Let $G_p$ with $p=\\frac{\\alpha}{d}$ be obtained from $G$ by including each edge of $G$ independently with probability $p$. We show that if $\\alpha<1$ then whp the maximum component size of $G_p$ is $O(\\log n)$ and if $\\alpha>1$ then $G_p$ contains a unique giant component of size $\\Omega(n)$, with all other components of size $O(\\log n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06643","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"}