|
The graph G is multiplicative if whenever there is a homomorphism of the product A ¡Ñ B of two graphs A and B into G then there is a homomorphism of A into G or a homomorphism of B to G.
Hedetniemies conjecture says every complete graph is multiplicative. It is not known if there are multiplicative graphs of arbitrary large chromatic number. Square free graphs are good candiates to provide multiplicative graphs of large chromatic number. So far we can prove that if the graphs A and B contain a triangle in every component and A ¡Ñ B has a homomorphism into a square free graph G then thereis a homomorphism of A into G or there is a homomorphism of B into G. |