Edge partitions of the Rado graph (Q1375697)

The Rado graph \(\mathcal R\) is the unique countable graph with the mapping extension property. It is known that coloring the edge set of \(\mathcal R\) by a finite number of colors there need not be a one-colored copy of \(\mathcal R\) in the resulting graph. The authors show that a two-colored copy of \(\mathcal R\) will appear.