{"paper":{"title":"Chi-boundedness of graph classes excluding wheel vertex-minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hojin Choi, O-joung Kwon, Paul Wollan, Sang-il Oum","submitted_at":"2017-02-25T08:11:39Z","abstract_excerpt":"A class of graphs is $\\chi$-bounded if there exists a function $f:\\mathbb N\\rightarrow \\mathbb N$ such that for every graph $G$ in the class and an induced subgraph $H$ of $G$, if $H$ has no clique of size $q+1$, then the chromatic number of $H$ is less than or equal to $f(q)$. We denote by $W_n$ the wheel graph on $n+1$ vertices. We show that the class of graphs having no vertex-minor isomorphic to $W_n$ is $\\chi$-bounded. This generalizes several previous results; $\\chi$-boundedness for circle graphs, for graphs having no $W_5$ vertex-minors, and for graphs having no fan vertex-minors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07851","kind":"arxiv","version":3},"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"}