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A graph is total threshold colorable if there exist integers $r,t$ such that for every $N \\subseteq E(G)$, $G$ admits an $(r,t)$-threshold-coloring with respect to $N$. We show that every prism is total threshold colorable, and that the Petersen graph is total threshold colorable. In contrast to this fact we show th"},"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":"1608.02332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-08T06:38:10Z","cross_cats_sorted":[],"title_canon_sha256":"029d42d0bbf7354e34e8d8c9ee12cec2b969cb1da24d940b3ea1eca43d711c18","abstract_canon_sha256":"75ba1af91d1a1394a7adbb623b587e3ae54dfe8d8da09c82150aeeaf6b56f381"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:40.456505Z","signature_b64":"5sXt9/FsaWZYi7s3DfiFMXqnMKlgovnnfj4lNU8bnoLFFLQSih64nazgoq7e5ESS+tkXpGImA4lnB4N3iP6bCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69ff3d3ed7ac45c540d1ed87e25b0fe79e56ed8972c1fd16a6099db0f2c15e20","last_reissued_at":"2026-05-18T01:09:40.456100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:40.456100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Threshold Colorings of Prisms and the Petersen Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gasper Fijavz, Matthias Kriesell","submitted_at":"2016-08-08T06:38:10Z","abstract_excerpt":"Let $G$ be a graph, $r \\geq t$ integers, and $N \\subseteq E(G)$. 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