arXiv:1805.02715 Abstract | arXiv Analytics

arXiv:1805.02715 [math.CO]Abstract References Reviews Resources

Anti-van der Waerden Numbers of Graph Products

Hunter Rehm, Alex Schulte, Nathan Warnberg

Published 2018-05-07Version 1

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.

Comments: 15 pages, 3 figures

Categories: math.CO

Keywords: anti-van der waerden number, graph products, cartesian product, upper bound, conjecture

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