  A graph $G$ of order $n$ is said to be $k$-factor-critical
  for integers $1\leq k < n$, if the removal of any $k$
  vertices results in a graph with a perfect matching.
  A $k$-factor-critical graph $G$
  is called minimal if for any edge $e\in E(G)$, $G-e$ is not
$k$-factor-critical.
  In 1998, O. Favaron and M. Shi conjectured that every minimal
$k$-factor-critical graph
  of order $n$ has the minimum degree $k+1$ and confirmed it for $k=1, n-2,
n-4$ and $n-6$.
  By using a novel approach, we have confirmed it for $k = n - 8$ in a previous
paper.
  Continuing this method, we prove the conjecture to be true for $k=n-10$ in
this paper.
