{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JUBLJUD5VTH6PI5XCAYBI44333","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":"7916a047811d4782ff3ffc916eba751f44be3e8379d748f845061e50a749da2d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-06T04:16:44Z","title_canon_sha256":"a99b20b926aaab3a3f6e56a62b4097a39b71577bbc1ee150c7f518bf43883afa"},"schema_version":"1.0","source":{"id":"1202.1046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1046","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1046v1","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1046","created_at":"2026-05-18T04:03:05Z"},{"alias_kind":"pith_short_12","alias_value":"JUBLJUD5VTH6","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JUBLJUD5VTH6PI5X","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JUBLJUD5","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:4e99a600e6141f6a5ae59febda3eabfdb833cd955d080eec74545f623b39b236","target":"graph","created_at":"2026-05-18T04:03:05Z","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":"A harmonious coloring of $G$ is a proper vertex coloring of $G$ such that every pair of colors appears on at most one pair of adjacent vertices. The harmonious chromatic number of $G$, $h(G)$, is the minimum number of colors needed for a harmonious coloring of $G$. We show that if $T$ is a forest of order $n$ with maximum degree $\\Delta(T)\\geq \\frac{n+2}{3}$, then $$h(T)=\n  \\Delta(T)+2, & if $T$ has non-adjacent vertices of degree $\\Delta(T)$;\n  \\Delta(T)+1, & otherwise.\n  $$ Moreover, the proof yields a polynomial-time algorithm for an optimal harmonious coloring of such a forest.","authors_text":"Alexandr Kostochka, Jaehoon Kim, Saieed Akbari","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-06T04:16:44Z","title":"Harmonious Coloring of Trees with Large Maximum Degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1046","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":"sha256:05b452fdf81342347de80e9658bfa60ee989109d2f3ce71f8027cf3505a0ed8c","target":"record","created_at":"2026-05-18T04:03:05Z","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":"7916a047811d4782ff3ffc916eba751f44be3e8379d748f845061e50a749da2d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-06T04:16:44Z","title_canon_sha256":"a99b20b926aaab3a3f6e56a62b4097a39b71577bbc1ee150c7f518bf43883afa"},"schema_version":"1.0","source":{"id":"1202.1046","kind":"arxiv","version":1}},"canonical_sha256":"4d02b4d07daccfe7a3b7103014739bdec8cb08c630d355cfed5f843450288645","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d02b4d07daccfe7a3b7103014739bdec8cb08c630d355cfed5f843450288645","first_computed_at":"2026-05-18T04:03:05.269991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:05.269991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E8SbGiMSJz6/61ma/KnVWpwZI7t154HUoW/j7emc8B3L/reudl7GqoidLzTrySN3L4cmo1TKiIrFWURnbBk+Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:05.270765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05b452fdf81342347de80e9658bfa60ee989109d2f3ce71f8027cf3505a0ed8c","sha256:4e99a600e6141f6a5ae59febda3eabfdb833cd955d080eec74545f623b39b236"],"state_sha256":"c1cd0b5624ea39bdf8907b25cc1f1a03b44756d32256b2da11f3ca868897a414"}