  A graph is $1$-$planar$ if it can be drawn in the plane so that each edge is
crossed by at most one other edge. Moreover, a 1-planar graph $G$ is $optimal$
if it satisfies $|E(G)|=4|V(G)|-8$. J. Fujisawa et al. [16] first considered
matching extension of optimal 1-planar graphs, obtained that each optimal
1-planar graph of even order is 1-extendable and characterized 2-extendable
optimal 1-planar graphs and 3-matchings extendable to perfect matchings as
well. In this short paper, we prove that no optimal $1$-planar graph is
3-extendable. Further we mainly obtain that no 1-planar graph is 5-extendable
by the discharge method and also construct a 4-extendable 1-planar graph.
Finally we get that no 1-planar graph is 7-factor-critical and no optimal
1-planar graph is 6-factor-critical.
