Characterizing all $K_4$-free well-edge-dominated graphs of girth 3
Combinatorics
2026-01-08 v2
Abstract
Given a graph , a set of edges is an edge dominating set if all edges in are either in or adjacent to an edge in . is said to be well-edge-dominated if every minimal edge dominating set is also minimum. In 2022, it was proven that there are precisely three nonbipartite, well-edge-dominated graphs with girth at least four. Then in 2025, a characterization of all well-edge-dominated graphs containing exactly one triangle was found. In this paper, we characterize all well-edge-dominated graphs that contain a triangle and yet are -free.
Cite
@article{arxiv.2511.06095,
title = {Characterizing all $K_4$-free well-edge-dominated graphs of girth 3},
author = {Sarah E. Anderson and Kirsti Kuenzel},
journal= {arXiv preprint arXiv:2511.06095},
year = {2026}
}