Triangle-free graphs with diameter 2
Combinatorics
2024-06-04 v1
Abstract
There are finitely many graphs with diameter and girth 5. What if the girth 5 assumption is relaxed? Apart from stars, are there finitely many triangle-free graphs with diameter and no subgraph? This question is related to the existence of triangle-free strongly regular graphs, but allowing for a range of co-degrees gives the question a more extremal flavour. More generally, for fixed and , are there infinitely many twin-free triangle-free -free graphs with diameter 2? This paper presents partial results regarding these questions, including computational results, potential Cayley-graph and probabilistic constructions.
Keywords
Cite
@article{arxiv.2406.00246,
title = {Triangle-free graphs with diameter 2},
author = {Alice Devillers and Nina Kamčev and Brendan McKay and Padraig Ó Catháin and Gordon Royle and Geertrui Van de Voorde and Ian Wanless and David R. Wood},
journal= {arXiv preprint arXiv:2406.00246},
year = {2024}
}