Iteration of the mincut graph operator
Combinatorics
2025-01-28 v1
Abstract
A graph operator is a mapping which maps every graph from some class of graphs to a new graph . In this paper, we introduce and study the properties of the mincut operator, specifically the effects of iteration of the operator. We show that the property of being super edge-connected and regular is both necessary and sufficient for a graph to remain fixed under the mincut operator. Furthermore, we show that no graph diverges under iteration of this operator. We conclude by stating further research questions on the mincut operator.
Keywords
Cite
@article{arxiv.2501.15883,
title = {Iteration of the mincut graph operator},
author = {Christo Kriel and Eunice Mphako-Banda},
journal= {arXiv preprint arXiv:2501.15883},
year = {2025}
}