21 Jun 2019
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Berikkyzy Zhanar
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Schulte Alex
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Sprangel Elizabeth
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Walker Shanise
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Warnberg Nathan
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Young Michael
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.(read more)