Communication lower bounds via the chromatic number

We present a new method for obtaining lower bounds on communication complexity. Our method is based on associating with a binary function f a graph G(f) such that log chi(G(f)) captures N-0(f) + N-1(f). Here chi(G) denotes the chromatic number of G, and N-0(f) and N-1(f) denote, respectively, the nondeterministic communication complexity of (f) over bar and f. Thus log chi(G(f)) is a lower bound on the deterministic as well as zero-error randomized communication complexity of f. Our characterization opens the possibility of using various relaxations of the chromatic number as lower bound techniques for communication complexity. In particular, we show how various (known) lower bounds can be derived by employing the clique number, the Lovasz v-function, and graph entropy lower bounds on the chromatic number.