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arXiv · 1802.01509

Anti-van der Waerden numbers on Graphs

Zhanar Berikkyzy·Alex Schulte·Elizabeth Sprangel·Shanise Walker·Nathan Warnberg·Michael Young
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Abstract

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 for which general bounds are obtained based on the radius and diameter of a graph. The general bounds are improved for trees and Cartesian products and exact values are determined for some classes of graphs. Larger k-term arithmetic progressions are considered and a connection between the Ramsey number of paths and the anti-van der Waerden number of graphs is established.

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Zhanar Berikkyzy, Alex Schulte, Elizabeth Sprangel, Shanise Walker, Nathan Warnberg, Michael Young. 2018-02-05. Anti-van der Waerden numbers on Graphs. https://arxiv.org/abs/1802.01509

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