Anti-van der Waerden numbers on Graphs
Combinatorics
2019-06-25 v2
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.
Keywords
Cite
@article{arxiv.1802.01509,
title = {Anti-van der Waerden numbers on Graphs},
author = {Zhanar Berikkyzy and Alex Schulte and Elizabeth Sprangel and Shanise Walker and Nathan Warnberg and Michael Young},
journal= {arXiv preprint arXiv:1802.01509},
year = {2019}
}