Maximal Digraphs With Respect to Primitive Positive Constructibility
Combinatorics
2022-10-11 v2 Rings and Algebras
Abstract
We study the class of all finite directed graphs up to primitive positive constructability. The resulting order has a unique greatest element, namely the graph with one vertex and no edges. The graph has a unique greatest lower bound, namely the graph with two vertices and one directed edge. Our main result is a complete description of the greatest lower bounds of ; we call these graphs submaximal. We show that every graph that is not equivalent to and is below one of the submaximal graphs.
Cite
@article{arxiv.2103.08625,
title = {Maximal Digraphs With Respect to Primitive Positive Constructibility},
author = {Florian Starke and Manuel Bodirsky},
journal= {arXiv preprint arXiv:2103.08625},
year = {2022}
}