{"paper":{"title":"Signed graphs with two negative edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eckhard Steffen, Edita Rollov\\'a, Michael Schubert","submitted_at":"2016-04-27T13:07:57Z","abstract_excerpt":"The presented paper studies the flow number $F(G,\\sigma)$ of flow-admissible signed graphs $(G,\\sigma)$ with two negative edges. We restrict our study to cubic graphs, because for each non-cubic signed graph $(G,\\sigma)$ there is a set ${\\cal G}(G,\\sigma)$ of cubic graphs such that $F(G, \\sigma) \\leq \\min \\{F(H,\\sigma_H) : (H,\\sigma_H) \\in {\\cal G}(G)\\}$. We prove that $F(G,\\sigma) \\leq 6$ if $(G,\\sigma)$ contains a bridge and $F(G,\\sigma) \\leq 7$ in general. We prove better bounds, if there is an element $(H,\\sigma_H)$ of ${\\cal G}(G,\\sigma)$ which satisfies some additional conditions. In par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08053","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"}