Ron Aharoni (Technion, Haifa): Cooperative colorings

 Given a family G_1, \ldots ,G_m of graphs on the same vertex set V, a
{\em cooperative coloring} is a choice of sets I_1, \ldots ,I_m, such that
I_j is independent in G_j (j \le m), and \bigcup I_j=V.
When G_1=\ldots =G_m=G then this is plainly an m-coloring of G. Very little
is known about cooperative colorings. For example, let f(d) be the minimal
number m such that if \Delta(G_j) \le d for all j\le m then there is a
cooperative coloring. A daring conjecture is that f(d)\le d+2, but we
only know that f(d) \le 2d. In the talk I will present several old and new
results on the subject.