  We study a combinatorial problem called Minimum Maximal Matching, where we
are asked to find in a general graph the smallest that can not be extended. We
show that this problem is hard to approximate with a constant smaller than 2,
assuming the Unique Games Conjecture.
  As a corollary we show, that Minimum Maximal Matching in bipartite graphs is
hard to approximate with constant smaller than $\frac{4}{3}$, with the same
assumption. With a stronger variant of the Unique Games Conjecture --- that is
Small Set Expansion Hypothesis --- we are able to improve the hardness result
up to the factor of $\frac{3}{2}$.
