The general position number of integer lattices

Sandi Klavžar and Gregor Rus

Applied Mathematics and Computation, 2021, vol. 390, issue C

Abstract: The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic. The n-dimensional grid graph P∞n is the Cartesian product of n copies of the two-way infinite path P∞. It is proved that if n∈N, then gp(P∞n)=22n−1. The result was earlier known only for n ∈ {1, 2} and partially for n=3.

Keywords: General position problem; Cartesian product of graphs; Integer lattice; Erdős-Szekeres theorem (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320306172

DOI: 10.1016/j.amc.2020.125664

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