 Examples of non-multiplicative graphs can be constructed from two graphs "G" and "H" that are not comparable in the homomorphism order (that is, neither "G"→"H" nor "H"→"G" holds).In this case, letting "K"="G"×"H", we trivially have "G"×"H"→"K", but neither "G" nor "H" can admit a homomorphism into "K", since composed with the projection "K"→"H" or "K"→"G" it would give a contradiction.Since the tensor product of graphs is the category-theoretic product in the category of graphs (with graphs as objects and homomorphisms as arrows), the conjecture can be rephrased in terms of the following construction on graphs "K" and "G".