A phase transition in Erd\H{o}s-Barak random graphs

/ Authors

Gilles Blanchard, Nicolas Curien, K. Krause, Alexander G. Reisach

/ Abstract

We study monotone paths in Erd\H{o}s-R\'enyi random graphs on numbered vertices. Benjamini&Tzalik established a phase transition at $p = \frac{\log n}{n}$ for this model. We refine the critical value to $p = \frac{\log n - \log \log n }{n}$ and identify the critical window of order $\Theta(1/n)$.

A phase transition in Erd\H{o}s-Barak random graphs

/ Authors

Gilles Blanchard, Nicolas Curien, K. Krause, Alexander G. Reisach

/ Abstract

We study monotone paths in Erd\H{o}s-R\'enyi random graphs on numbered vertices. Benjamini&Tzalik established a phase transition at $p = \frac{\log n}{n}$ for this model. We refine the critical value to $p = \frac{\log n - \log \log n }{n}$ and identify the critical window of order $\Theta(1/n)$.