Compatible forts and maximum nullity of a graph
Document Type
Article
Publication Date
2025
Department/School
Mathematics
Publication Title
Graphs an dCombinatorics
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.
Link to Published Version
Recommended Citation
Furst, V., Hutchens, J., Mitchell, L., & Zhang, Y. (2025). Compatible forts and maximum nullity of a graph. Graphs and Combinatorics, 41, 56. https://doi.org/10.1007/s00373-025-02919-4
Comments
L. Mitchell is a faculty member in EMU's Department of Mathematics and Statistics.