{"paper":{"title":"Excluding induced subdivisions of the bull and related graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Scott, Irena Penev, Maria Chudnovsky, Nicolas Trotignon","submitted_at":"2013-09-05T11:18:30Z","abstract_excerpt":"For any graph $H$, let ${\\rm Forb}^*(H)$ be the class of graphs with no induced subdivision of $H$. It was conjectured in [A.D. Scott, Induced trees in graphs of large chromatic number, {\\em Journal of Graph Theory}, 24:297--311, 1997] that, for every graph $H$, there is a function $f_H:\\mathbb{N} \\rightarrow \\mathbb{R}$ such that for every graph $G \\in {\\rm Forb}^*(H)$, $\\chi(G) \\leq f_H(\\omega(G))$. We prove this conjecture for several graphs $H$, namely the paw (a triangle with a pendant edge), the bull (a triangle with two vertex-disjoint pendant edges), and what we call a \"necklace,\" that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1312","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"}