{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:L23BRXPBKY5HLSVMAM6MBGP5BR","short_pith_number":"pith:L23BRXPB","schema_version":"1.0","canonical_sha256":"5eb618dde1563a75caac033cc099fd0c5efbb1623a5af7c1aea56cdfa47b0748","source":{"kind":"arxiv","id":"1502.03132","version":2},"attestation_state":"computed","paper":{"title":"Coloring the square of a sparse graph $G$ with almost $\\Delta(G)$ colors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Matthew Yancey","submitted_at":"2015-02-10T21:44:25Z","abstract_excerpt":"For a graph $G$, let $G^2$ be the graph with the same vertex set as $G$ and $xy \\in E(G^2)$ when $x \\neq y$ and $d_G(x,y) \\leq 2$. Bonamy, L\\'ev\\^{e}que, and Pinlou conjectured that if $mad (G) < 4 - \\frac{2}{c+1}$ and $\\Delta(G)$ is large, then $\\chi_\\ell(G^2) \\leq \\Delta(G) + c$. We prove that if $c \\geq 3$, $mad (G) < 4 - \\frac{4}{c+1}$, and $\\Delta(G)$ is large, then $\\chi_\\ell(G^2) \\leq \\Delta(G) + c$. Dvo\\v{r}\\'ak, Kr\\'{a}\\soft{l}, Nejedl\\'{y}, and \\v{S}krekovski conjectured that $\\chi(G^2) \\leq \\Delta(G) +2$ when $\\Delta(G)$ is large and $G$ is planar with girth at least $5$; our result"},"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":"1502.03132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-10T21:44:25Z","cross_cats_sorted":[],"title_canon_sha256":"46d62a985ae28919470776978f49eb4ff526c5f0006c4c7bcb630a90e026e5fd","abstract_canon_sha256":"d7c28a292ff5722c6eac6e260dcb1a1e1428ca51ad976208c4be744eaaf8f5c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:58.160122Z","signature_b64":"G+XiRjMKLZ9kkGF15WuC+hV8/pxmAkKFD+NbM630/IJvgPfT0gWTBXHrJbK7Kz7K2cYAK87+/GdsWjtvnYvAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5eb618dde1563a75caac033cc099fd0c5efbb1623a5af7c1aea56cdfa47b0748","last_reissued_at":"2026-05-18T02:18:58.159603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:58.159603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coloring the square of a sparse graph $G$ with almost $\\Delta(G)$ colors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Matthew Yancey","submitted_at":"2015-02-10T21:44:25Z","abstract_excerpt":"For a graph $G$, let $G^2$ be the graph with the same vertex set as $G$ and $xy \\in E(G^2)$ when $x \\neq y$ and $d_G(x,y) \\leq 2$. Bonamy, L\\'ev\\^{e}que, and Pinlou conjectured that if $mad (G) < 4 - \\frac{2}{c+1}$ and $\\Delta(G)$ is large, then $\\chi_\\ell(G^2) \\leq \\Delta(G) + c$. We prove that if $c \\geq 3$, $mad (G) < 4 - \\frac{4}{c+1}$, and $\\Delta(G)$ is large, then $\\chi_\\ell(G^2) \\leq \\Delta(G) + c$. Dvo\\v{r}\\'ak, Kr\\'{a}\\soft{l}, Nejedl\\'{y}, and \\v{S}krekovski conjectured that $\\chi(G^2) \\leq \\Delta(G) +2$ when $\\Delta(G)$ is large and $G$ is planar with girth at least $5$; our result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03132","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":"1502.03132","created_at":"2026-05-18T02:18:58.159687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.03132v2","created_at":"2026-05-18T02:18:58.159687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03132","created_at":"2026-05-18T02:18:58.159687+00:00"},{"alias_kind":"pith_short_12","alias_value":"L23BRXPBKY5H","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"L23BRXPBKY5HLSVM","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"L23BRXPB","created_at":"2026-05-18T12:29:29.992203+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2210.05915","citing_title":"Coloring, List Coloring, and Painting Squares of Graphs (and other related problems)","ref_index":192,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L23BRXPBKY5HLSVMAM6MBGP5BR","json":"https://pith.science/pith/L23BRXPBKY5HLSVMAM6MBGP5BR.json","graph_json":"https://pith.science/api/pith-number/L23BRXPBKY5HLSVMAM6MBGP5BR/graph.json","events_json":"https://pith.science/api/pith-number/L23BRXPBKY5HLSVMAM6MBGP5BR/events.json","paper":"https://pith.science/paper/L23BRXPB"},"agent_actions":{"view_html":"https://pith.science/pith/L23BRXPBKY5HLSVMAM6MBGP5BR","download_json":"https://pith.science/pith/L23BRXPBKY5HLSVMAM6MBGP5BR.json","view_paper":"https://pith.science/paper/L23BRXPB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.03132&json=true","fetch_graph":"https://pith.science/api/pith-number/L23BRXPBKY5HLSVMAM6MBGP5BR/graph.json","fetch_events":"https://pith.science/api/pith-number/L23BRXPBKY5HLSVMAM6MBGP5BR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L23BRXPBKY5HLSVMAM6MBGP5BR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L23BRXPBKY5HLSVMAM6MBGP5BR/action/storage_attestation","attest_author":"https://pith.science/pith/L23BRXPBKY5HLSVMAM6MBGP5BR/action/author_attestation","sign_citation":"https://pith.science/pith/L23BRXPBKY5HLSVMAM6MBGP5BR/action/citation_signature","submit_replication":"https://pith.science/pith/L23BRXPBKY5HLSVMAM6MBGP5BR/action/replication_record"}},"created_at":"2026-05-18T02:18:58.159687+00:00","updated_at":"2026-05-18T02:18:58.159687+00:00"}