Bicliques and Eigenvalues

A biclique in a graph ? is a complete bipartite subgraph of ?. We give bounds for the maximum number of edges in a biclique in terms of the eigenvalues of matrix representations of ?. These bounds show a strong similarity with Lovasz's bound ?(?) for the Shannon capacity of ?. Motivated by this similarity we investigate bicliques and the bounds in certain product graphs.

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