Hedetniemi's conjecture and the retracts of a product of graphs

We show that every core graph with a primitive automorphism group has the p roperty that whenever it is a retract of a, product of connected graphs, it is a retract of a factor. The example of Kneser graphs shows that the hypo thesis that the factors are connected is essential. In the case of complete graphs, our result has already been shown in [4,17], and it is an instance where Hedetniemi's conjecture is known to hold. In fact, our work is motiv ated by a reinterpretation of Hedetniemi's conjecture in terms of products and retracts.