A Sufficient condition for DP-4-colorability

DP-coloring of a simple graph is a generalization of list coloring, and also a generalization of signed coloring of signed graphs. It is known that for each $k\in \{3,4,5,6\}$, every planar graph without $C_k$ is 4-choosable. Furthermore, Jin, Kang, and Steffen \cite{JKS} showed that for each $k \in {3, 4, 5, 6}$,everysignedplanargraphwithout$C_k$ is signed 4-choosable. In this paper, we show that for each $k\in \{3,4,5,6\}$, every planar graph without $C_k$ is 4-DP-colorable, which is an extension of the above results.