Title: Mixed Cages,
Abstract: We introduce the notion of a $[z, r; g]$-mixed cage. A $[z, r; g]$-mixed cage
is a mixed graph $G$, $z$-regular by arcs, $r$-regular by edges, with girth $g$
and minimum order. In this paper we prove the existence of $[z, r ;g]$-mixed
cages and exhibit families of mixed cages for some specific values. We also
give lower and upper bounds for some choices of $z, r$ and $g$. In particular
we present the first results on $[z,r;g]$- mixed cages for $z=1$ and any $r\geq
1$ and $g\geq 3$, and for any $z\geq 1$, $r=1$ and $g=4$.