Year: 2026
Type: preprint
Abstract: We study the structure of random $d$-regular triangle-free graphs and show that a sharp phase transition occurs at $d=\frac{\sqrt 3}{2}\sqrt{n \log n}$. For smaller $d$, asymptotically almost surely the graph is non-bipartite, whereas for greater $d$, asymptotically almost surely the graph is bipartite.
Source: arXiv (Cornell University)
Authors: DeCamillis, Gregory, Gao, Pu
Institution: University of Waterloo
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213496006