Anti-van der Waerden numbers on Graphs

Alex Schulte, Nathan Warnberg, Michael Young

Published 2018-02-05Version 1

In this paper arithmetic progressions on the integers and the integers modulo n are extended to graphs. This allows for the definition of the anti-van der Waerden number of a graph. Much of the focus of this paper is on 3-term arithmetic progressions. With general results, bounds obtained using distance parameters, and determining exact values for classes of graphs, including trees and cartesian products of graphs.