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Abstract: "We call a bipartite graph homogeneous if every finite partial automorphism which respects left and right can be extended to a total automorphism. We classify all countable homogeneous bipartite graphs. A ([kappa], [lambda]) bipartite graph is a bipartite graph with left side of size [kappa] and right side of size [lambda]. We show that there is always a homogeneous (NΓéÇ,2[superscript n0]) bipartite graph (thus answering negatively a question by Kupitz and Perles), and that depending on the underlying set theory all homogeneous (NΓéÇ, NΓéü) bipartite graphs may be isomorphic, or there may be 2[superscript N┬╣] many isomorphism types of (NΓéÇ, NΓéü) homogeneous graphs."