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We also give bounds on the minimum number of colors needed for any $r$ in terms of the genus of the graph: for sufficiently large $r$, every graph with genus $g$ is $r$-dynamically $((r+1)(g+5)+3)$-colorable when $g\\leq2$ and $r$-dynamically $((r+1)(2g+"},"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":"1511.03983","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-12T17:40:16Z","cross_cats_sorted":[],"title_canon_sha256":"114f9908f51daedc3755be72fc208f2a386322dc7db0d75c5bca96f8f6285f83","abstract_canon_sha256":"5a6d2d7742b3bd9326267594e443ed6071f179c910bfb51b69176e369a7ddaee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:06.324426Z","signature_b64":"H/IdM5is5RZ/lMPry9xIsrGpQpVY6Q7+/xRVDeevysZjniOm8KuKuCDWOsN1LJSA9Jfj8TwKk9HoDwbrhpB4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19e66240b9a98ade16cca3042d64e3eef89a44c196245d4854a3abe33c78882a","last_reissued_at":"2026-05-18T01:27:06.323899Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:06.323899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamic coloring parameters for graphs with given genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin Reiniger, Jennifer Wise, Sarah Loeb, Thomas Mahoney","submitted_at":"2015-11-12T17:40:16Z","abstract_excerpt":"A proper vertex coloring of a graph $G$ is $r$-dynamic if for each $v\\in V(G)$, at least $\\min\\{r,d(v)\\}$ colors appear in $N_G(v)$. 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