{"paper":{"title":"Nowhere-zero flows on signed regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Eckhard Steffen, Michael Schubert","submitted_at":"2013-07-05T09:31:30Z","abstract_excerpt":"We study the flow spectrum ${\\cal S}(G)$ and the integer flow spectrum $\\overline{{\\cal S}}(G)$ of signed $(2t+1)$-regular graphs. We show that if $r \\in {\\cal S}(G)$, then $r = 2+\\frac{1}{t}$ or $r \\geq 2 + \\frac{2}{2t-1}$. Furthermore, $2 + \\frac{1}{t} \\in {\\cal S}(G)$ if and only if $G$ has a $t$-factor. If $G$ has a 1-factor, then $3 \\in \\overline{{\\cal S}}(G)$, and for every $t \\geq 2$, there is a signed $(2t+1)$-regular graph $(H,\\sigma)$ with $ 3 \\in \\overline{{\\cal S}}(H)$ and $H$ does not have a 1-factor.\n  If $G$ $(\\not = K_2^3)$ is a cubic graph which has a 1-factor, then $\\{3,4\\} \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1562","kind":"arxiv","version":4},"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"}