Author

Hemanshu Kaul

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Preprint Sep 2026

Covering Families for DP-Coloring of Cartesian Products with Complete Bipartite Graphs

A famous folklore result in list coloring demonstrating that the gap between the list chromatic number and chromatic number of a graph can be arbitrarily large is: $\chi_{\ell}(K_{l,t}) = 1+l$ if and only if $t \geq l^l$. DP-coloring (also called correspondence coloring) is a well-studied generalization of list colorin...

Hemanshu Kaul, Jeffrey A. Mudrock, Emily A. Psyhogios et al. · 0 citations

Preprint Jul 2026

The unlabeled list color function of disconnected graphs

Given a graph $G$, its chromatic polynomial $P (G, k)$ counts proper $k$-colorings, while the corresponding list color function $P_{\ell} (G, k)$ counts the minimum number of proper colorings across all assignments of $k$ colors to each vertex. While it is clear that $P_{\ell} (G, k) \leq P (G, k)$, Donner showed in 19...

Hemanshu Kaul, Jeffrey A. Mudrock, Armin Straub · 0 citations