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arXiv · 2609.17958

When are random regular triangle-free graphs bipartite?

Gregory DeCamillis·Pu Gao
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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.

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Gregory DeCamillis, Pu Gao. 2026-09-16. When are random regular triangle-free graphs bipartite?. https://arxiv.org/abs/2609.17958

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