{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:CEMGE73IXVQB2BXWHCER4C7SSX","short_pith_number":"pith:CEMGE73I","schema_version":"1.0","canonical_sha256":"1118627f68bd601d06f638891e0bf295f2b8433e2b66f1625fd048628839960c","source":{"kind":"arxiv","id":"1010.5624","version":2},"attestation_state":"computed","paper":{"title":"Locally identifying coloring of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Aline Parreau (IF), Louis Esperet (G-SCOP), Mickael Montassier (LaBRI), Pascal Ochem (LRI), Sylvain Gravier (IF)","submitted_at":"2010-10-27T09:34:56Z","abstract_excerpt":"We introduce the notion of locally identifying coloring of a graph. A proper vertex-coloring c of a graph G is said to be locally identifying, if for any adjacent vertices u and v with distinct closed neighborhood, the sets of colors that appear in the closed neighborhood of u and v are distinct. Let $\\chi_{lid}(G)$ be the minimum number of colors used in a locally identifying vertex-coloring of G. In this paper, we give several bounds on $\\chi_{lid}$ for different families of graphs (planar graphs, some subclasses of perfect graphs, graphs with bounded maximum degree) and prove that deciding "},"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":"1010.5624","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-10-27T09:34:56Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a0348ac4bec034f74a048ca559ff2c2784c96c67d243cd48915e00883d134b16","abstract_canon_sha256":"8d5e373bcfc31add734e23f2fa59699b1d21b2d56b3397b824712e286d221967"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:08.749084Z","signature_b64":"VpeGtHuqAV1ceyrUfjlmeFPbIzmzqrSjRBm2I2KO1XB1SHYk5Q7eoJ4tkUnWw66PZ3sErpkG0M/qYYqKkngdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1118627f68bd601d06f638891e0bf295f2b8433e2b66f1625fd048628839960c","last_reissued_at":"2026-05-18T01:32:08.748415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:08.748415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Locally identifying coloring of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Aline Parreau (IF), Louis Esperet (G-SCOP), Mickael Montassier (LaBRI), Pascal Ochem (LRI), Sylvain Gravier (IF)","submitted_at":"2010-10-27T09:34:56Z","abstract_excerpt":"We introduce the notion of locally identifying coloring of a graph. A proper vertex-coloring c of a graph G is said to be locally identifying, if for any adjacent vertices u and v with distinct closed neighborhood, the sets of colors that appear in the closed neighborhood of u and v are distinct. Let $\\chi_{lid}(G)$ be the minimum number of colors used in a locally identifying vertex-coloring of G. In this paper, we give several bounds on $\\chi_{lid}$ for different families of graphs (planar graphs, some subclasses of perfect graphs, graphs with bounded maximum degree) and prove that deciding "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5624","kind":"arxiv","version":2},"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":"1010.5624","created_at":"2026-05-18T01:32:08.748531+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.5624v2","created_at":"2026-05-18T01:32:08.748531+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5624","created_at":"2026-05-18T01:32:08.748531+00:00"},{"alias_kind":"pith_short_12","alias_value":"CEMGE73IXVQB","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CEMGE73IXVQB2BXW","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CEMGE73I","created_at":"2026-05-18T12:26:05.355336+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/CEMGE73IXVQB2BXWHCER4C7SSX","json":"https://pith.science/pith/CEMGE73IXVQB2BXWHCER4C7SSX.json","graph_json":"https://pith.science/api/pith-number/CEMGE73IXVQB2BXWHCER4C7SSX/graph.json","events_json":"https://pith.science/api/pith-number/CEMGE73IXVQB2BXWHCER4C7SSX/events.json","paper":"https://pith.science/paper/CEMGE73I"},"agent_actions":{"view_html":"https://pith.science/pith/CEMGE73IXVQB2BXWHCER4C7SSX","download_json":"https://pith.science/pith/CEMGE73IXVQB2BXWHCER4C7SSX.json","view_paper":"https://pith.science/paper/CEMGE73I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.5624&json=true","fetch_graph":"https://pith.science/api/pith-number/CEMGE73IXVQB2BXWHCER4C7SSX/graph.json","fetch_events":"https://pith.science/api/pith-number/CEMGE73IXVQB2BXWHCER4C7SSX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CEMGE73IXVQB2BXWHCER4C7SSX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CEMGE73IXVQB2BXWHCER4C7SSX/action/storage_attestation","attest_author":"https://pith.science/pith/CEMGE73IXVQB2BXWHCER4C7SSX/action/author_attestation","sign_citation":"https://pith.science/pith/CEMGE73IXVQB2BXWHCER4C7SSX/action/citation_signature","submit_replication":"https://pith.science/pith/CEMGE73IXVQB2BXWHCER4C7SSX/action/replication_record"}},"created_at":"2026-05-18T01:32:08.748531+00:00","updated_at":"2026-05-18T01:32:08.748531+00:00"}