Well-failed graphs
Combinatorics
2025-02-03 v1
Abstract
In this paper we begin the study of well-failed graphs, that is, graphs in which every maximal failed zero forcing set is a maximum failed zero forcing set, or equivalently, in which every minimal fort is a minimum fort. We characterize trees that are well-failed. Along the way, we prove that the set of vertices in a graph that are not in any minimal fort is identical to the set of vertices that are in no minimal zero forcing set, which allows us to characterize vertices in a tree that are in no minimal fort.
Keywords
Cite
@article{arxiv.2501.19357,
title = {Well-failed graphs},
author = {Bonnie Jacob},
journal= {arXiv preprint arXiv:2501.19357},
year = {2025}
}