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Infinite homogeneous bipartite graphs with unequal sides

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journal contribution
posted on 01.01.1992, 00:00 authored by Martin Goldstern, Rami Grossberg, Menachem Kojman
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 (N₀,2[superscript n0]) bipartite graph (thus answering negatively a question by Kupitz and Perles), and that depending on the underlying set theory all homogeneous (N₀, N₁) bipartite graphs may be isomorphic, or there may be 2[superscript N¹] many isomorphism types of (N₀, N₁) homogeneous graphs."


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