 The main result of , independently improved by Poljak, James H. Schmerl, and Zhu, states that if the function "f"("n") is bounded, then it is bounded by at most 9.Thus a proof of Hedetniemi's conjecture for 10-chromatic graphs would already imply the Weak Hedetniemi Conjecture for all graphs.The conjecture is studied in the more general context of graph homomorphisms, especially because of interesting relations to the category of graphs (with graphs as objects and homomorphisms as arrows).