In this paper we introduce and study a new problem named \emph{min-max edge
q-coloring} which is motivated by applications in wireless mesh networks. The
input of the problem consists of an undirected graph and an integer q. The
goal is to color the edges of the graph with as many colors as possible such
that: (a) any vertex is incident to at most q different colors, and (b) the
maximum size of a color group (i.e. set of edges identically colored) is
minimized. We show the following results: 1. Min-max edge q-coloring is
NP-hard, for any q≥2. 2. A polynomial time exact algorithm for min-max
edge q-coloring on trees. 3. Exact formulas of the optimal solution for
cliques and almost tight bounds for bicliques and hypergraphs. 4. A non-trivial
lower bound of the optimal solution with respect to the average degree of the
graph. 5. An approximation algorithm for planar graphs.Comment: 16 pages, 5 figure