{"paper":{"title":"A generalization of Noel-Reed-Wu Theorem to signed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jianguo Qian, Wei Wang","submitted_at":"2018-10-23T09:38:46Z","abstract_excerpt":"Let $\\Sigma$ be a signed graph where two edges joining the same pair of vertices with opposite signs are allowed. The zero-free chromatic number $\\chi^*(\\Sigma)$ of $\\Sigma$ is the minimum even integer $2k$ such that $G$ admits a proper coloring $f\\colon\\,V(\\Sigma)\\mapsto \\{\\pm 1,\\pm 2,\\ldots,\\pm k\\}$. The zero-free list chromatic number $\\chi^*_l(\\Sigma)$ is the list version of zero-free chromatic number. $\\Sigma$ is called zero-free chromatic-choosable if $\\chi^*_l(\\Sigma)=\\chi^*(\\Sigma)$. We show that if $\\Sigma$ has at most $\\chi^*(\\Sigma)+1$ vertices then $\\Sigma$ is zero-free chromatic-c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09741","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"}