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Kostochka and Woodall conjectured that for every graph, the list-chromatic number of $G^2$ equals the chromatic number of $G^2$, that is $\\chi_l(G^2)=\\chi(G^2)$ for all $G$. If true, this conjecture (together with Thomassen's result) implies that every planar graph $G$ with $\\Delta(G)=3$ satisfies $\\chi_l(G^2)\\leq 7$. We prove that every"},"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":"1503.00157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-28T17:04:23Z","cross_cats_sorted":[],"title_canon_sha256":"6c2aa05448a80c6a4d3e4b97242d47cf3417d50e1e63c33e65f9de7e3bf1859b","abstract_canon_sha256":"285d9317c47caaad8bf90031390fa3407cffb82cb92a777cec0eb651f055ee50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:55.035759Z","signature_b64":"itSp+mdJx9yCjNeyDSyX0NWnU+MQOMANzIACuhTgD5PnjUWiJnALnL0CXc1evheG44sFczHhCuJMoDv+4f1dDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"622bf02b4fa2123d628e72d9c0ec88c6b22ec25b6b9ad9735be54c4fc426135e","last_reissued_at":"2026-05-18T02:25:55.035341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:55.035341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"List-coloring the Square of a Subcubic Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel W. Cranston, Seog-Jin Kim","submitted_at":"2015-02-28T17:04:23Z","abstract_excerpt":"The {\\em square} $G^2$ of a graph $G$ is the graph with the same vertex set as $G$ and with two vertices adjacent if their distance in $G$ is at most 2. Thomassen showed that every planar graph $G$ with maximum degree $\\Delta(G)=3$ satisfies $\\chi(G^2)\\leq 7$. Kostochka and Woodall conjectured that for every graph, the list-chromatic number of $G^2$ equals the chromatic number of $G^2$, that is $\\chi_l(G^2)=\\chi(G^2)$ for all $G$. If true, this conjecture (together with Thomassen's result) implies that every planar graph $G$ with $\\Delta(G)=3$ satisfies $\\chi_l(G^2)\\leq 7$. 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