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Non-null cycles in group labeled graphs generalize several well-known graph structures, including odd cycles.\n  In this paper, we prove that non-null cycles on Group Labeled Graphs have the hal"},"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":"1703.02866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-03-08T15:16:05Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"2c8c09716f201fedcbcaad6efa5a836887c6913760f47aedc3b6b976b2c5d2d5","abstract_canon_sha256":"35d89b494823c7ac2e78bc27d82071f2ecca344c3eb3061ecd0d1d4fc0eaf9b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:05.445551Z","signature_b64":"lWucgILmz8zBZOmwtzRG8tR8pz+XFpKqYG2y3raem9rDufsxPPK4byzjI8pa3FibCHk7qguR/dZ29Os0ez9jCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a0062588c0774e6167ad161662369953d3d09a1df05fc7bc0f6a397a442b448","last_reissued_at":"2026-05-18T00:49:05.445122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:05.445122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Half-integral Erd\\\"os-P\\'osa Property for Non-null Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Daniel Lokshtanov, M. 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