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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\\} \\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.1562","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-05T09:31:30Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"5ec6674b1f6aa8e1dd5c393f400693b270d42bbf5d8a1fd37298d3eb558d21da","abstract_canon_sha256":"d648ea3f06095bff3665ddfbf9fdce9a0e2d819b230c480605c16c3f28e4945b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:42.064627Z","signature_b64":"13AccblgYoNgVPHUaJBzR5ZZ3e1SOiP5l5GYUbqMAVWkLw9JS+hWp8oo1Zxudo2ZUmJb0plW/sNp3QUlgtkiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09c1eda30b86443f00299ea37b9263b1b651db5b20505285b33c124f69db731f","last_reissued_at":"2026-05-18T01:32:42.063865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:42.063865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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