{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QH4NAKLD4RNGFWGGPLGZ7QSINU","short_pith_number":"pith:QH4NAKLD","schema_version":"1.0","canonical_sha256":"81f8d02963e45a62d8c67acd9fc2486d14b0780d1821d87cab6dfae472dd099d","source":{"kind":"arxiv","id":"1809.03582","version":1},"attestation_state":"computed","paper":{"title":"Conflict-free connection number of random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ran Gu, Xueliang Li","submitted_at":"2018-09-10T20:29:04Z","abstract_excerpt":"An edge-colored graph $G$ is conflict-free connected if any two of its vertices are connected by a path which contains a color used on exactly one of its edges. The conflict-free connection number of a connected graph $G$, denoted by $cfc(G)$, is the smallest number of colors needed in order to make $G$ conflict-free connected. In this paper, we show that almost all graphs have the conflict-free connection number 2. More precisely, let $G(n,p)$ denote the Erd\\H{o}s-R\\'{e}nyi random graph model, in which each of the $\\binom{n}{2}$ pairs of vertices appears as an edge with probability $p$ indepe"},"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":"1809.03582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-10T20:29:04Z","cross_cats_sorted":[],"title_canon_sha256":"9bd7f6ac9574ec274e2ea0a7863763f4c43f3470c0cd972190a14464b060817d","abstract_canon_sha256":"4c4ed4e5ee2baf97674178fbff0742d051acc7a34090a2d73ce329c8d82b7ed0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:00.406195Z","signature_b64":"krcnj4rtzK1MOFnzvyJlGhOgT2pIdLENil6oHML4uTUqL6aoRXkthuePoTDMepZUgDNCsT9uP8TOqhSNBsjpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81f8d02963e45a62d8c67acd9fc2486d14b0780d1821d87cab6dfae472dd099d","last_reissued_at":"2026-05-18T00:06:00.405597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:00.405597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conflict-free connection number of random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ran Gu, Xueliang Li","submitted_at":"2018-09-10T20:29:04Z","abstract_excerpt":"An edge-colored graph $G$ is conflict-free connected if any two of its vertices are connected by a path which contains a color used on exactly one of its edges. The conflict-free connection number of a connected graph $G$, denoted by $cfc(G)$, is the smallest number of colors needed in order to make $G$ conflict-free connected. In this paper, we show that almost all graphs have the conflict-free connection number 2. More precisely, let $G(n,p)$ denote the Erd\\H{o}s-R\\'{e}nyi random graph model, in which each of the $\\binom{n}{2}$ pairs of vertices appears as an edge with probability $p$ indepe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03582","kind":"arxiv","version":1},"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":"1809.03582","created_at":"2026-05-18T00:06:00.405683+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.03582v1","created_at":"2026-05-18T00:06:00.405683+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03582","created_at":"2026-05-18T00:06:00.405683+00:00"},{"alias_kind":"pith_short_12","alias_value":"QH4NAKLD4RNG","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QH4NAKLD4RNGFWGG","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QH4NAKLD","created_at":"2026-05-18T12:32:46.962924+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/QH4NAKLD4RNGFWGGPLGZ7QSINU","json":"https://pith.science/pith/QH4NAKLD4RNGFWGGPLGZ7QSINU.json","graph_json":"https://pith.science/api/pith-number/QH4NAKLD4RNGFWGGPLGZ7QSINU/graph.json","events_json":"https://pith.science/api/pith-number/QH4NAKLD4RNGFWGGPLGZ7QSINU/events.json","paper":"https://pith.science/paper/QH4NAKLD"},"agent_actions":{"view_html":"https://pith.science/pith/QH4NAKLD4RNGFWGGPLGZ7QSINU","download_json":"https://pith.science/pith/QH4NAKLD4RNGFWGGPLGZ7QSINU.json","view_paper":"https://pith.science/paper/QH4NAKLD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.03582&json=true","fetch_graph":"https://pith.science/api/pith-number/QH4NAKLD4RNGFWGGPLGZ7QSINU/graph.json","fetch_events":"https://pith.science/api/pith-number/QH4NAKLD4RNGFWGGPLGZ7QSINU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QH4NAKLD4RNGFWGGPLGZ7QSINU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QH4NAKLD4RNGFWGGPLGZ7QSINU/action/storage_attestation","attest_author":"https://pith.science/pith/QH4NAKLD4RNGFWGGPLGZ7QSINU/action/author_attestation","sign_citation":"https://pith.science/pith/QH4NAKLD4RNGFWGGPLGZ7QSINU/action/citation_signature","submit_replication":"https://pith.science/pith/QH4NAKLD4RNGFWGGPLGZ7QSINU/action/replication_record"}},"created_at":"2026-05-18T00:06:00.405683+00:00","updated_at":"2026-05-18T00:06:00.405683+00:00"}