  To any integer matrix $A$ one can associate a matroid structure consisting of
a graph and another integer matrix $A_B$. The connected components of this
graph are called bouquets. We prove that bouquets behave well with respect to
the $r$--th Lawrence liftings of matrices and we use it to prove that the
Markov and Graver complexities of $m\times n$ matrices of rank $d$ may be
arbitrarily large for $n\geq 4$ and $d\leq n-2$. In contrast, we show they are
bounded in terms of $n$ and the largest absolute value $a$ of any entry of $A$.
