The general position number of digraphs
Combinatorics
2026-04-20 v1
Abstract
The general position number for graphs ask for largest vertex subsets such that no three vertices are contained on a common shortest path. We examine this problem in the setting of directed graphs. We provide bounds for the general position number of digraphs, show that the problem is NP-complete for oriented graphs, investigate the problem for some important families of digraphs such as circulant digraphs, Kautz digraphs and permutation digraphs, and study the general position numbers obtained from all orientations of an undirected graph.
Keywords
Cite
@article{arxiv.2604.15909,
title = {The general position number of digraphs},
author = {Ullas Chandran S. V. and Gabriele Di Stefano and Grahame Erskine and Haritha S and Elias John Thomas and James Tuite},
journal= {arXiv preprint arXiv:2604.15909},
year = {2026}
}