  A {\it clutter} (or {\it antichain} or {\it Sperner family}) $L$ is a pair
$(V,E)$, where $V$ is a finite set and $E$ is a family of subsets of $V$ none
of which is a subset of another. Usually, the elements of $V$ are called {\it
vertices} of $L$, and the elements of $E$ are called {\it edges} of $L$. A
subset $s_e$ of an edge $e$ of a clutter is called {\it recognizing} for $e$,
if $s_e$ is not a subset of another edge. The {\it hardness} of an edge $e$ of
a clutter is the ratio of the size of $e\textrm{'s}$ smallest recognizing
subset to the size of $e$. The hardness of a clutter is the maximum hardness of
its edges. We study the hardness of clutters arising from independent sets and
matchings of graphs.
