  A multi-graph $G$ on $n$ vertices is $(k,\ell)$-sparse if every subset of
$n'\leq n$ vertices spans at most $kn'- \ell$ edges. $G$ is {\em tight} if, in
addition, it has exactly $kn - \ell$ edges. For integer values $k$ and $\ell
\in [0, 2k)$, we characterize the $(k,\ell)$-sparse graphs via a family of
simple, elegant and efficient algorithms called the $(k,\ell)$-pebble games.
