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Let $G$ be a multipartite graph with partition $V_1, V_2,\ldots, V_k$ of$V(G)$. Let $d_{i,j}$ denote the edge density of the pair $(V_i, V_j)$. Anindependent transversal is an independent set of $G$ with exactly one vertex ineach $V_i$. In this paper, we prove an asymptotically sharp upper bound on themaximum number of independent transversals given the $d_{i,j}$'s.

A Sharp Bound on the Maximum Number of Independent Transversals