{"paper":{"title":"On the maximum running time in graph bootstrap percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"B\\'ela Bollob\\'as, Julian Sahasrabudhe, Micha{\\l} Przykucki, Oliver Riordan","submitted_at":"2015-10-24T01:13:35Z","abstract_excerpt":"Graph bootstrap percolation is a simple cellular automaton introduced by Bollob\\'as in 1968. Given a graph $H$ and a set $G \\subseteq E(K_n)$ we initially \"infect\" all edges in $G$ and then, in consecutive steps, we infect every $e \\in K_n$ that completes a new infected copy of $H$ in $K_n$. We say that $G$ percolates if eventually every edge in $K_n$ is infected. The extremal question about the size of the smallest percolating sets when $H = K_r$ was answered independently by Alon, Kalai and Frankl. Here we consider a different question raised more recently by Bollob\\'as: what is the maximum "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07096","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"}