{"paper":{"title":"The width of quadrangulations of the projective plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Louis Esperet, Mat\\v{e}j Stehl\\'ik","submitted_at":"2015-09-25T13:50:44Z","abstract_excerpt":"We show that every $4$-chromatic graph on $n$ vertices, with no two vertex-disjoint odd cycles, has an odd cycle of length at most $\\tfrac12\\,(1+\\sqrt{8n-7})$. Let $G$ be a non-bipartite quadrangulation of the projective plane on $n$ vertices. Our result immediately implies that $G$ has edge-width at most $\\tfrac12\\,(1+\\sqrt{8n-7})$, which is sharp for infinitely many values of $n$. We also show that $G$ has face-width (equivalently, contains an odd cycle transversal of cardinality) at most $\\tfrac14(1+\\sqrt{16 n-15})$, which is a constant away from the optimal; we prove a lower bound of $\\sqr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07716","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"}