{"paper":{"title":"Fractional DP-Colorings of Sparse Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Anton Bernshteyn, Xuding Zhu","submitted_at":"2018-01-22T20:29:48Z","abstract_excerpt":"DP-coloring (also known as correspondence coloring) is a generalization of list coloring developed recently by Dvo\\v{r}\\'{a}k and Postle. In this paper we introduce and study the fractional DP-chromatic number $\\chi_{DP}^\\ast(G)$. We characterize all connected graphs $G$ such that $\\chi_{DP}^\\ast(G) \\leqslant 2$: they are precisely the graphs with no odd cycles and at most one even cycle. By a theorem of Alon, Tuza, and Voigt, the fractional list-chromatic number $\\chi_\\ell^\\ast(G)$ of any graph $G$ equals its fractional chromatic number $\\chi^\\ast(G)$. This equality does not extend to fractio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07307","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"}