{"paper":{"title":"Bootstrap Percolation on Degenerate Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marinus Gottschau","submitted_at":"2016-05-23T13:00:13Z","abstract_excerpt":"In this paper we focus on $r$-neighbor bootstrap percolation, which is a process on a graph where initially a set $A_0$ of vertices gets infected. Now subsequently, an uninfected vertex becomes infected if it is adjacent to at least $r$ infected vertices. Call $A_f$ the set of vertices that is infected after the process stops. More formally set $A_t:=A_{t-1}\\cup \\{v\\in V: |N(v)\\cap A_{t-1}|\\geq r\\}$, where $N(v)$ is the neighborhood of $v$. Then $A_f=\\bigcup_{t>0} A_t$. We deal with finite graphs only and denote by $n$ the number of vertices. We are mainly interested in the size of the final s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07002","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"}