... several properties of a maximal IC-coloring f of Km,n.Proposition 3.3. If f is a maximal IC-coloring of G = (A, B) = Km,n, then all thecolorings of vertices of G are distinct.Proof. Suppose, ... proof is complete. the electronic journal of combinatorics 15 (2008), #R43 2 n ≥ 3, we have f4= 10 ≤ 3 · 24−2− 24−(n+2)− 1. This is a contradiction to that f isa maximal IC-coloring of ... havethe electronic journal of combinatorics 15 (2008), #R43 9 By Proposition 3.1, it contradicts to the assumption that f is a maximal IC-coloring of G and we have the proof of (3). Finally, we prove...