{"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 $t \\geq k^k$. We show that $\\chi_{DP} (K_{k,t}) = k+1$ if $t \\geq 1 + (k^k/k!)("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09141","kind":"arxiv","version":1},"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"}