Consider a graph obtained by taking an edge disjoint union of $k$ complete bipartite graphs, Alon, Saks, and Seymour conjectured that such graphs have chromatic number at most k+1. This well known conjecture remained open for almost twenty years. In this talk, we will show a counterexample to this conjecture. This construction will also lead to some related results in combinatorial geometry and communication complexity. In particular, it implies a nontrivial lower bound of the non-deterministic communication complexity of the ``clique versus independent set'' problem.\\ Joint work with Benny Sudakov.