{"paper":{"title":"The chromatic spectrum of signed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eckhard Steffen, Yingli Kang","submitted_at":"2015-10-02T14:43:59Z","abstract_excerpt":"The chromatic number $\\chi((G,\\sigma))$ of a signed graph $(G,\\sigma)$ is the smallest number $k$ for which there is a function $c : V(G) \\rightarrow \\mathbb{Z}_k$ such that $c(v) \\not= \\sigma(e) c(w)$ for every edge $e = vw$. Let $\\Sigma(G)$ be the set of all signatures of $G$. We study the chromatic spectrum $\\Sigma_{\\chi}(G) = \\{\\chi((G,\\sigma))\\colon\\ \\sigma \\in \\Sigma(G)\\}$ of $(G,\\sigma)$. Let $M_{\\chi}(G) = \\max\\{\\chi((G,\\sigma))\\colon\\ \\sigma \\in \\Sigma(G)\\}$, and $m_{\\chi}(G) = \\min\\{\\chi((G,\\sigma))\\colon\\ \\sigma \\in \\Sigma(G)\\}$. We show that $\\Sigma_{\\chi}(G) = \\{k : m_{\\chi}(G) \\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00614","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"}