{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JCZXQZBU53NGNXAVXMY6PZ7HXB","short_pith_number":"pith:JCZXQZBU","schema_version":"1.0","canonical_sha256":"48b3786434eeda66dc15bb31e7e7e7b86b471e10a90cbf6f7e1afc1f020af378","source":{"kind":"arxiv","id":"1503.08191","version":3},"attestation_state":"computed","paper":{"title":"Fractional triangle decompositions in graphs with large minimum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fran\\c{c}ois Dross","submitted_at":"2015-03-27T19:22:06Z","abstract_excerpt":"A triangle decomposition of a graph is a partition of its edges into triangles. A fractional triangle decomposition of a graph is an assignment of a non-negative weight to each of its triangles such that the sum of the weights of the triangles containing any given edge is one. We prove that for all $\\epsilon > 0$, every large enough graph graph on $n$ vertices with minimum degree at least $(0.9 + \\epsilon)n$ has a fractional triangle decomposition. This improves a result of Garaschuk that the same result holds for graphs with minimum degree at least $0.956n$. Together with a recent result of B"},"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":"1503.08191","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-27T19:22:06Z","cross_cats_sorted":[],"title_canon_sha256":"2c4be5f6a69b66edab8c6d465a63d6e8055ecad5e35487994f4f1c5f2f9f4e34","abstract_canon_sha256":"d63aea22b15ee176ffd445155864581c8fc983e30294702a9ecf6def937e3298"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:33.644438Z","signature_b64":"RyAwcI4xOLJ+GchSLM81IsrvEVxibFyzMnE3Gpo45xdcZjayVNzuv/pKP19GIg0tFBL0f0tHcfzLltEYX/4/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48b3786434eeda66dc15bb31e7e7e7b86b471e10a90cbf6f7e1afc1f020af378","last_reissued_at":"2026-05-18T01:36:33.644045Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:33.644045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional triangle decompositions in graphs with large minimum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fran\\c{c}ois Dross","submitted_at":"2015-03-27T19:22:06Z","abstract_excerpt":"A triangle decomposition of a graph is a partition of its edges into triangles. A fractional triangle decomposition of a graph is an assignment of a non-negative weight to each of its triangles such that the sum of the weights of the triangles containing any given edge is one. We prove that for all $\\epsilon > 0$, every large enough graph graph on $n$ vertices with minimum degree at least $(0.9 + \\epsilon)n$ has a fractional triangle decomposition. This improves a result of Garaschuk that the same result holds for graphs with minimum degree at least $0.956n$. Together with a recent result of B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08191","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.08191","created_at":"2026-05-18T01:36:33.644109+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.08191v3","created_at":"2026-05-18T01:36:33.644109+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08191","created_at":"2026-05-18T01:36:33.644109+00:00"},{"alias_kind":"pith_short_12","alias_value":"JCZXQZBU53NG","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JCZXQZBU53NGNXAV","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JCZXQZBU","created_at":"2026-05-18T12:29:27.538025+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JCZXQZBU53NGNXAVXMY6PZ7HXB","json":"https://pith.science/pith/JCZXQZBU53NGNXAVXMY6PZ7HXB.json","graph_json":"https://pith.science/api/pith-number/JCZXQZBU53NGNXAVXMY6PZ7HXB/graph.json","events_json":"https://pith.science/api/pith-number/JCZXQZBU53NGNXAVXMY6PZ7HXB/events.json","paper":"https://pith.science/paper/JCZXQZBU"},"agent_actions":{"view_html":"https://pith.science/pith/JCZXQZBU53NGNXAVXMY6PZ7HXB","download_json":"https://pith.science/pith/JCZXQZBU53NGNXAVXMY6PZ7HXB.json","view_paper":"https://pith.science/paper/JCZXQZBU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.08191&json=true","fetch_graph":"https://pith.science/api/pith-number/JCZXQZBU53NGNXAVXMY6PZ7HXB/graph.json","fetch_events":"https://pith.science/api/pith-number/JCZXQZBU53NGNXAVXMY6PZ7HXB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JCZXQZBU53NGNXAVXMY6PZ7HXB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JCZXQZBU53NGNXAVXMY6PZ7HXB/action/storage_attestation","attest_author":"https://pith.science/pith/JCZXQZBU53NGNXAVXMY6PZ7HXB/action/author_attestation","sign_citation":"https://pith.science/pith/JCZXQZBU53NGNXAVXMY6PZ7HXB/action/citation_signature","submit_replication":"https://pith.science/pith/JCZXQZBU53NGNXAVXMY6PZ7HXB/action/replication_record"}},"created_at":"2026-05-18T01:36:33.644109+00:00","updated_at":"2026-05-18T01:36:33.644109+00:00"}