DP‐coloring Cartesian products of graphs

DP-coloring (also called correspondence coloring) is a generalization of list coloring introduced by Dvo\v{r}\'{a}k and Postle in 2015. Motivated results related to Cartesian products graphs, we initiate the study DP-chromatic number, $\chi_{DP}$, same. We show that $\chi_{DP}(G \square H) \leq \text{min}\{\chi_{DP}(G) + \text{col}(H), \chi_{DP}(H) \text{col}(G) \} - 1$ where $\text{col}(H)$ number graph $H$. focus on building tools for lower bound arguments H)$ use them sharpness above its various forms. Our illustrate DP color function $G$, analogue chromatic polynomial, essential product including following question extends problem classical result gap between number: given any $G$ $k \in \mathbb{N}$, what smallest $t$ which K_{k,t})= \chi_{DP}(G) k$?