Reducts of the random bipartite graph

Let $Γ$ be the random bipartite graph, a countable graph with two infinite sides, edges randomly distributed between the sides, but no edges within a side. In this paper, we investigate the reducts of $Γ$ that preserve sides. We classify the closed permutation subgroups containing the group $Aut(Γ)^*$, where $Aut(Γ)^*$ is the group of all isomorphisms and anti-isomorphisms of $Γ$ preserving the two sides. Our results rely on a combinatorial theorem of Nešetřil-Rödl and a strong finite submodel property for $Γ$.

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