  We call a bipartite graph {\it homogeneous} if every finite partial
automorphism which respects left and right can be extended to a total
automorphism.
  A $(\kappa,{\lambda} )$ bipartite graph is a bipartite graph with left side
of size $\kappa$ and right side of size ${\lambda}$. We show, using a theorem
of Hrushovski on finite graphs, that there is a homogeneous
$({\aleph_0},2^{\aleph_0} )$ bipartite graph of girth 4 (thus answering
negatively a question by Kupitz and Perles), and that depending on the
underlying set theory all homogeneous $({\aleph_0},\aleph_1)$ bipartite graphs
may be isomorphic, or there may be $2^{\aleph_1}$ many isomorphism types of
$(\aleph_0,\aleph_1)$ homogeneous graphs.
