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Mathematics  2011 

Reducts of the Generalized Random Bipartite Graph

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Abstract:

Let \Gamma be the generalized random bipartite graph that has two sides Rl and Rr with edges for every pair of vertices between R1 and Rr but no edges within each side, where all the edges are randomly colored by three colors P1; P2; P3. In this paper, we investigate the reducts of \Gamma that preserve Rl and Rr, and classify the closed permutation subgroups in Sym(Rl)\timesSym(Rr) containing the group Aut(\Gamma). Our results rely on a combinatorial theorem of Nesetril-Rodl and the strong finite submodel property of the random bipartite graph.

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