The level of nonmultiplicativity of graphs Original Research Article

We introduce a parameter called the level of nonmultiplicativity of a graph, which is related to Hedetniemiʹs conjecture. We show that this parameter is equal to the number of factors in a factorization of the graph into a product of multiplicative graphs. Apart from the known multiplicative graphs, no graph is known to have a finite level of nonmultiplicativity. We show that the countably infinite complete graph Kℵ0 has an infinite level of nonmultiplicativity and that there exist Kneser graphs with arbitrarily high levels of nonmultiplicativity.