Compatible Forts and Maximum Nullity of a Graph
Combinatorics
2024-07-08 v1
Abstract
We consider bounds on maximum nullity of a graph via transversal numbers of compatible collections of forts. Results include generalizations of theorems from symmetric to combinatorially symmetric matrices, special bases of matrix nullspaces derived from transversal sets, and examples of issues that arise when considering only minimal forts and how to avoid them. We also show an important difference between constructing symmetric and combinatorially symmetric matrices associated to a graph whose nullspaces are supported on collections of disjoint forts.
Cite
@article{arxiv.2407.03492,
title = {Compatible Forts and Maximum Nullity of a Graph},
author = {Veronika Furst and John Hutchens and Lon Mitchell and Yaqi Zhang},
journal= {arXiv preprint arXiv:2407.03492},
year = {2024}
}