  A graph $G$ with four or more vertices is called bicritical if the removal of
any pair of distinct vertices of $G$ results in a graph with a perfect
matching. A bicritical graph is minimal if the deletion of each edge results in
a non-bicritical graph. Recently, Y. Zhang et al. and F. Lin et al.
respectively showed that bicritical graphs without removable edges and minimal
bricks have at least four cubic vertices. In this note, we show that minimal
bicritical graphs also have at least four cubic vertices, so confirming O.
Favaron and M. Shi's conjecture in the case of $k=2$ on minimal $k$-factor
critical graphs.
