Let 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 that preserve sides. We classify the closed permutation subgroups containing the group , where is the group of all isomorphisms and anti-isomorphisms of preserving the two sides. Our results rely on a combinatorial theorem of Nešetřil and Rödl and a strong finite submodel property for .
"Reducts of the Random Bipartite Graph." Notre Dame J. Formal Logic 54 (1) 33 - 46, 2013. https://doi.org/10.1215/00294527-1731371