  A graph $G=(V,E)$ is a $k$-critical graph if $G$ is not $(k -1)$-colorable
but $G-e$ is $(k-1)$-colorable for every $e\in E(G)$. In this paper, we
construct a family of 4-critical planar graphs with $n$ vertices and
$\frac{7n-13}{3}$ edges. As a consequence, this improved the bound for the
maximum edge density obtained by Abbott and Zhou. We conjecture that this is
the largest edge density for a 4-critical planar graph.
