Chromatic numbers of the strong product of odd cycles

The problem of determining the chromatic numbers of the strong product of cycles is considered. A construction is given proving χ (G) = 2p +1 for a product of p odd cycles of lengths at least 2p +1. Several consequences are discussed. In particular, it is proved that the strong product of p factors has chromatic number at most 2p +1 provided that each factor admits a homomorphism to sufficiently long odd cycle Cmi, mi ≥ 2p +1.