Moving through Cartesian products, coronas and joins in general position
Combinatorics
2025-10-16 v2
Abstract
The general position problem asks for large sets of vertices such that no three vertices of the set lie on a common shortest path. Recently a dynamic version of this problem was defined, called the \emph{mobile general position problem}, in which a collection of robots must visit all the vertices of the graph whilst remaining in general position. In this paper we investigate this problem in the context of Cartesian products, corona products and joins, giving upper and lower bounds for general graphs and exact values for families including grids, cylinders, Hamming graphs and prisms of trees.
Keywords
Cite
@article{arxiv.2505.00535,
title = {Moving through Cartesian products, coronas and joins in general position},
author = {Sandi Klavžar and Aditi Krishnakumar and Dorota Kuziak and Ethan Shallcross and James Tuite and Ismael G. Yero},
journal= {arXiv preprint arXiv:2505.00535},
year = {2025}
}