Abstract
Bollobás, Erdős, and Szemerédi (1975) [1] investigated a tripartite generalization of the Zarankiewicz problem: what minimum degree forces a tripartite graph with n vertices in each part to contain an octahedral graph K3(2)? They proved that n+2−1/2n3/4 suffices and suggested it could be weakened to n+cn1/2 for some constant c>0. In this note we show that their method only gives n+(1+o(1))n11/12 and provide many constructions that show that if true, n+cn1/2 is best possible.
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