The channel assignment problem is the problem of efficiently assigning frequencies to radio transmitters located at various places such that communications do not interfere. Griggs and Yeh [5] introduced a variation of the channel assignment problem known as the L(2, 1)-colorings of graphs. An L(2, 1)-coloring of a graph G = (V, E) is a vertex coloring f: V(G) → {0, 1, 2,…, k}, k ≥ 2 such that |f(u) – f(v)| ≥ 2 for all uv ∊ E(G) and |f(u) – f(v)| ≥ 1 if d(u, v) = 2. The span of G, λ(G), is the smallest integer k for which G has an L(2, 1)-coloring. An L(2, 1)-coloring f is irreducible if there does not exist an L(2, 1)-coloring g such that g(u) ≤ f(u) for all u ∊ V(G) and g(v) < f(v) for some v ∊ V(G). A span coloring is an L(2, 1)-coloring whose greatest color is λ(G). Let f be an L(2, 1)-coloring that uses colors from 0 to k. Then h ∊ (0, k) is a hole if there is no vertex v in V(G) such that f(v) = h. In this paper, we investigate maximum number of holes in span colorings of certain classes of graphs. We give exact values for the maximum number of holes in a span coloring of a path, cycle, star, complete bipartite graph and characterize complete graphs in terms of their maximum number of holes. Upper bounds for an arbitrary graph and other classes of graphs are also given.