{"paper":{"title":"Bounds on the Burning Number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anthony Bonato, Dieter Rautenbach, Jeannette Janssen, St\\'ephane Bessy","submitted_at":"2015-11-18T23:30:01Z","abstract_excerpt":"Motivated by a graph theoretic process intended to measure the speed of the spread of contagion in a graph, Bonato, Janssen, and Roshanbin [Burning a Graph as a Model of Social Contagion, Lecture Notes in Computer Science 8882 (2014) 13-22] define the burning number $b(G)$ of a graph $G$ as the smallest integer $k$ for which there are vertices $x_1,\\ldots,x_k$ such that for every vertex $u$ of $G$, there is some $i\\in \\{ 1,\\ldots,k\\}$ with ${\\rm dist}_G(u,x_i)\\leq k-i$, and ${\\rm dist}_G(x_i,x_j)\\geq j-i$ for every $i,j\\in \\{ 1,\\ldots,k\\}$.\n  For a connected graph $G$ of order $n$, they prove "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06023","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"}