Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3
Combinatorics
2026-02-02 v4
Abstract
In this short note it is shown that every graph of diameter 2 and minimum degree at least 3 contains a cycle of length 4 or 8. This result contributes to the study of the Erd\H{o}s-Gy\'arf\'as Conjecture by confirming it for the class of diameter-2 graphs.
Cite
@article{arxiv.2508.19302,
title = {Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3},
author = {Avery Carr},
journal= {arXiv preprint arXiv:2508.19302},
year = {2026}
}
Comments
12 pages, 10 figures. Accepted for publication; to appear in the Bulletin of the Institute of Combinatorics and its Applications (BICA)