{"paper":{"title":"Nowhere-zero flows on signed eulerian graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edita M\\'a\\v{c}ajov\\'a, Martin \\v{S}koviera","submitted_at":"2014-08-07T20:07:50Z","abstract_excerpt":"This paper is devoted to a detailed study of nowhere-zero flows on signed eulerian graphs. We generalise the well-known fact about the existence of nowhere-zero $2$-flows in eulerian graphs by proving that every signed eulerian graph that admits an integer nowhere-zero flow has a nowhere-zero $4$-flow. We also characterise signed eulerian graphs with flow number $2$, $3$, and $4$, as well as those that do not have an integer nowhere-zero flow. Finally, we discuss the existence of nowhere-zero $A$-flows on signed eulerian graphs for an arbitrary abelian group~$A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1703","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"}