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On the other hand, there are several properties of the DP-chromatic number that shows that it differs with the list chromatic number. In this note we show one such property. It is well known that $\\chi_\\ell (K_{k,t}) = k+1$ if and only if $t \\geq k^k$. We show that $\\chi_{DP} (K_{k,t}) = k+1$ if $t \\geq 1 + (k^k/k!)("},"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":"1803.09141","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-24T18:00:13Z","cross_cats_sorted":[],"title_canon_sha256":"f78a94d0ae8bcd359708af6e1f81e66202889fe680b22b6a7c32290446a56125","abstract_canon_sha256":"abaeb0f1eb2367633d488c7a5bc130b0213109686ff7f2cfb369b6e6fc0218ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:12.521388Z","signature_b64":"x8B//36JQPomDksbUSpghKm+kWAoxKSbK5ugHDPI6ZIC3mnSMzbYMy8AIIiRs5yyBnTYy4Ag7hRNU9fgDQ7ABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50ce10eb67d7caf0b71da2945ff87bbf062f39d88750aec704cbb08723bf5b17","last_reissued_at":"2026-05-18T00:20:12.520939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:12.520939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on the DP-Chromatic Number of Complete Bipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jeffrey A. Mudrock","submitted_at":"2018-03-24T18:00:13Z","abstract_excerpt":"DP-coloring (also called correspondence coloring) is a generalization of list coloring recently introduced by Dvo\\v{r}\\'{a}k and Postle. Several known bounds for the list chromatic number of a graph $G$, $\\chi_\\ell(G)$, also hold for the DP-chromatic number of $G$, $\\chi_{DP}(G)$. On the other hand, there are several properties of the DP-chromatic number that shows that it differs with the list chromatic number. In this note we show one such property. It is well known that $\\chi_\\ell (K_{k,t}) = k+1$ if and only if $t \\geq k^k$. 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