{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EYMMNXOGEHEQQU463WFO4LIG4O","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":"6001f59729ed1dc3a3023c4ff1ba499a9330e90dcc13cfcb7a9763bd25e799b3","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-11-21T20:09:24Z","title_canon_sha256":"bfadfbb036a33c986e7d99f1cdaa5200c1b766ff51c0789cc9de30d41390f1e5"},"schema_version":"1.0","source":{"id":"0911.4199","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4199","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4199v5","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4199","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"pith_short_12","alias_value":"EYMMNXOGEHEQ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EYMMNXOGEHEQQU46","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EYMMNXOG","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:831c402c9925be2b80ac62f2d1e60db80f6b0962d550fbf2ffee43eed0e7fb21","target":"graph","created_at":"2026-05-18T00:51:30Z","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 2-hued coloring of a graph $G$ (also known as conditional $(k, 2)$-coloring and dynamic coloring) is a coloring such that for every vertex $v\\in V(G)$ of degree at least $2$, the neighbors of $v$ receive at least $2$ colors. The smallest integer $k$ such that $G$ has a 2-hued coloring with $ k $ colors, is called the {\\it 2-hued chromatic number} of $G$ and denoted by $\\chi_2(G)$. In this paper, we will show that if $G$ is a regular graph, then $ \\chi_{2}(G)- \\chi(G) \\leq 2 \\log _{2}(\\alpha(G)) +\\mathcal{O}(1) $ and if $G$ is a graph and $\\delta(G)\\geq 2$, then $ \\chi_{2}(G)- \\chi(G) \\leq 1+","authors_text":"Ali Dehghan, Arash Ahadi","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-11-21T20:09:24Z","title":"Upper bounds for the 2-hued chromatic number of graphs in terms of the independence number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4199","kind":"arxiv","version":5},"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:f9ea5785d38bb798e4a0dcfc83f3f730bd7e8c94136e0a1c310346ff0467b8d0","target":"record","created_at":"2026-05-18T00:51:30Z","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":"6001f59729ed1dc3a3023c4ff1ba499a9330e90dcc13cfcb7a9763bd25e799b3","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-11-21T20:09:24Z","title_canon_sha256":"bfadfbb036a33c986e7d99f1cdaa5200c1b766ff51c0789cc9de30d41390f1e5"},"schema_version":"1.0","source":{"id":"0911.4199","kind":"arxiv","version":5}},"canonical_sha256":"2618c6ddc621c908539edd8aee2d06e3a4442966ede00abcd7cc7dc0bf356252","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2618c6ddc621c908539edd8aee2d06e3a4442966ede00abcd7cc7dc0bf356252","first_computed_at":"2026-05-18T00:51:30.811561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:30.811561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"su+c4zXHUFiMAisFFfZfYZUlJ5GbkOzKYlEP12h8EbghTPc3H6G6t1lpx/xVUSrYPmxiGysE7wUOTI835cLMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:30.812071Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.4199","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9ea5785d38bb798e4a0dcfc83f3f730bd7e8c94136e0a1c310346ff0467b8d0","sha256:831c402c9925be2b80ac62f2d1e60db80f6b0962d550fbf2ffee43eed0e7fb21"],"state_sha256":"01d2c760ae9345b0910d92aef202472b1dd39334a81ab38011a1c9fc26d9e35f"}