{"paper":{"title":"Chromatic number of signed graphs with bounded maximum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sagnik Sen, Sandip Das, Soumen Nandi, Soumyajit Paul","submitted_at":"2016-03-31T12:36:29Z","abstract_excerpt":"A signed graph $ (G, \\Sigma)$ is a graph positive and negative ($\\Sigma $ denotes the set of negative edges). To re-sign a vertex $v$ of a signed graph $ (G, \\Sigma)$ is to switch the signs of the edges incident to $v$. If one can obtain $ (G, \\Sigma')$ by re-signing some vertices of $ (G, \\Sigma)$, then\n  $ (G, \\Sigma) \\equiv (G, \\Sigma')$.\n  A signed graphs $ (G, \\Sigma )$ admits an homomorphism to $ (H, \\Lambda )$ if there is a sign preserving vertex mapping from $(G,\\Sigma')$ to $(H, \\Lambda)$ for some $ (G, \\Sigma) \\equiv (G, \\Sigma')$.\n  The signed chromatic number $\\chi_{s}( (G, \\Sigma)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09557","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"}