English

Iteration of the mincut graph operator

Combinatorics 2025-01-28 v1

Abstract

A graph operator is a mapping ϕ\phi which maps every graph GG from some class of graphs to a new graph ϕ(G)\phi(G). 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}
}
R2 v1 2026-06-28T21:19:11.291Z