  In this paper, anti-van der Waerden numbers on Cartesian products of graphs
are investigated and a conjecture made by Schulte, et al (see arXiv:1802.01509)
is answered. In particular, the anti-van der Waerden number of the Cartesian
product of two graphs has an upper bound of four. This result is then used to
determine the anti-van der Waerden number for any Cartesian product of two
paths.
