Infinite homogeneous bipartite graphs with unequal sides Original Research Article

We call a bipartite graph homogeneous if every finite partial automorphism which respects left and right can be extended to a total automorphism. A (κ, λ) bipartite graph is a bipartite graph with left side of size κ and right side of size λ. We show that there is a homogeneous 0,20 bipartite graph of girth 4 (thus answering negatively a question by Kupitz and Perles), and that depending on the underlying set theory all homogeneous 0,1)bipartite graphs may be isomorphic, or there may be 21 many isomorphism types of (0,1 homogeneous graphs.