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On the hitting time of Hamiltonicity in bipartite Dirac graphs
Yiting Wang · 2026-06-10 · via math updates on arXiv.org

Let $\varepsilon\in (0,1/2]$ and let $G$ be a balanced bipartite graph on $2n$ vertices with minimum degree at least $(1/2 + \varepsilon)n$. Then, whp, the hitting time for minimum degree 2 coincides with the hitting time for Hamiltonicity. This extends Bollobás--Kohayakawa and gives a bipartite analogue of Johansson's theorem. As an immediate corollary, we deduce a sharp threshold result for Hamiltonicity in such graphs.

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