Reconfiguration of Minimum PSD Forcing Sets and Minimum Skew Forcing Sets
Combinatorics
2025-01-08 v1
Abstract
Reconfiguration graphs provide a way to represent relationships among solutions to a problem, and have been studied in many contexts. We investigate the reconfiguration graphs corresponding to minimum PSD forcing sets and minimum skew forcing sets. We present results for the structure and realizability of certain graph classes as token exchange and token sliding reconfiguration graphs. Additionally, we use a universal approach to establish structural properties for the reconfiguration graphs of many common graph parameters under these reconfiguration rules. Finally, we compare results on reconfiguration graphs for zero forcing variants.
Cite
@article{arxiv.2501.03642,
title = {Reconfiguration of Minimum PSD Forcing Sets and Minimum Skew Forcing Sets},
author = {Novi Bong and Mary Flagg and Mark Hunnell and John Hutchens and Ryan Moruzzi and Houston Schuerger and Ben Small},
journal= {arXiv preprint arXiv:2501.03642},
year = {2025}
}