{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5AVOB7UJW55WXKG5TH3AYBHZMW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9c323d06f902d1d7294b6db26a781faad75911f85e2e609d08a7442190489934","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-19T21:25:45Z","title_canon_sha256":"2f855297cfbabb8c3b30ca5771aba20c6c4ab0d4a4ba9f334f9fcf3de99e6671"},"schema_version":"1.0","source":{"id":"1404.4987","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4987","created_at":"2026-05-18T02:53:52Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4987v1","created_at":"2026-05-18T02:53:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4987","created_at":"2026-05-18T02:53:52Z"},{"alias_kind":"pith_short_12","alias_value":"5AVOB7UJW55W","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5AVOB7UJW55WXKG5","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5AVOB7UJ","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:1b59af2f16698431d20c679c123de883715b08df06299f4d21e7b1ea5e63eede","target":"graph","created_at":"2026-05-18T02:53:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the question of the existence of homomorphisms between $G_{n,p}$ and odd cycles when $p=c/n,\\,1<c\\leq 4$. We show that for any positive integer $\\ell$, there exists $\\epsilon=\\epsilon(\\ell)$ such that if $c=1+\\epsilon$ then w.h.p. $G_{n,p}$ has a homomorphism from $G_{n,p}$ to $C_{2\\ell+1}$ so long as its odd-girth is at least $2\\ell+1$. On the other hand, we show that if $c=4$ then w.h.p. there is no homomorphism from $G_{n,p}$ to $C_5$. Note that in our range of interest, $\\chi(G_{n,p})=3$ w.h.p., implying that there is a homomorphism from $G_{n,p}$ to $C_3$.","authors_text":"Alan Frieze, Wesley Pegden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-19T21:25:45Z","title":"Between 2- and 3-colorability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4987","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9947c5d7533306e17ca89b591e477730e2ca83fd585fe819106914a9a2a80198","target":"record","created_at":"2026-05-18T02:53:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9c323d06f902d1d7294b6db26a781faad75911f85e2e609d08a7442190489934","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-19T21:25:45Z","title_canon_sha256":"2f855297cfbabb8c3b30ca5771aba20c6c4ab0d4a4ba9f334f9fcf3de99e6671"},"schema_version":"1.0","source":{"id":"1404.4987","kind":"arxiv","version":1}},"canonical_sha256":"e82ae0fe89b77b6ba8dd99f60c04f965a92548f27efd63ca61603c1edc9b0236","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e82ae0fe89b77b6ba8dd99f60c04f965a92548f27efd63ca61603c1edc9b0236","first_computed_at":"2026-05-18T02:53:52.325862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:52.325862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9p5df97hA01HLfFSOrCUwTiBh/nx3vqv+EDLaJIBnMqMqcpI0n68Ve8vnykgK3QG6Qx94wblFXqn0wRrDFd5DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:52.326430Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4987","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9947c5d7533306e17ca89b591e477730e2ca83fd585fe819106914a9a2a80198","sha256:1b59af2f16698431d20c679c123de883715b08df06299f4d21e7b1ea5e63eede"],"state_sha256":"155399015b71fd22117cd17bb0666536910f80cebca06359bae4ad246288f9bb"}