Colorings of infinite graphs without one-colored rays

The R-chromatic number of a graph G is the least number of subsets of vertices forming a partition of V(G), and which induce subgraphs of G without infinite paths. For any integer n ≥ 2, we give sufficient conditions for a graph containing no subdivision of an infinite complete graph to have a R-chromatic number ≤ n. © 1996 John Wiley & Sons, Inc.