  A graph is 1-planar if it can be drawn in the plane such that each edge is
crossed at most once. A graph, together with a 1-planar drawing is called
1-plane. Brandenburg et al. showed that there are maximal 1-planar graphs with
only $\frac{45}{17}n + O(1)\approx 2.647n$ edges and maximal 1-plane graphs
with only $\frac{7}{3}n+O(1)\approx 2.33n$ edges. On the other hand, they
showed that a maximal 1-planar graph has at least $\frac{28}{13}n-O(1)\approx
2.15n-O(1)$ edges, and a maximal 1-plane graph has at least $2.1n-O(1)$ edges.
  We improve both lower bounds to $\frac{20n}{9}\approx 2.22n$.
