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We also confirm the conjecture that any facet of $CUTP_8$ is adjacent to a triangle facet.\n  The lists of facets for $K_{1,l,m}$ with $(l,m)=(4,4),("},"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":"1501.05407","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-22T06:58:09Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"6b1432480bd51f6a44b2afd337e506d836c4f7526b14619ff513d1da14ecb726","abstract_canon_sha256":"46b69a2e4ba47e8de668e03770a8083d44100196ab452614ef4108df62d99c6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:54.259876Z","signature_b64":"5UEJxzddA33Bayf1ly1hXx8XHHRAvnvWdAwHaRx7lm3a+6UOLgU2yOQyJlhJiey58oeCKJazFJDzomCiydfuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1529b2dea0df47b5e5098df4c6bd1463380b5b70aacbcc40f2ecee694bb662f","last_reissued_at":"2026-05-18T02:09:54.259151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:54.259151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enumeration of the facets of cut polytopes over some highly symmetric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Mathieu Dutour Sikiric, Michel Deza","submitted_at":"2015-01-22T06:58:09Z","abstract_excerpt":"We report here a computation giving the complete list of facets for the cut polytopes over several very symmetric graphs with $15-30$ edges, including $K_8$, $K_{3,3,3}$, $K_{1,4,4}$, $K_{5,5}$, some other $K_{l,m}$, $K_{1,l,m}$, $Prism_7, APrism_6$, M\\\"{o}bius ladder $M_{14}$, Dodecahedron, Heawood and Petersen graphs.\n  For $K_8$, it shows that the huge lists of facets of the cut polytope $CUTP_8$ and cut cone $CUT_8$, given in [CR] is complete. 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