Triangle percolation in mean field random graphs -- with PDE

TL;DR

This paper introduces a PDE-based approach to analyze the emergence of a giant component in triangle percolation on Erdős-Rényi graphs, providing precise critical times and component sizes.

Contribution

The paper presents a novel PDE method to determine critical phenomena in triangle percolation, advancing understanding of phase transitions in random graphs.

Findings

Identifies critical time for giant component emergence.

Calculates size of the giant component at criticality.

Provides a PDE framework for percolation analysis.

Abstract

We apply a PDE-based method to deduce the critical time and the size of the giant component of the ``triangle percolation'' on the Erd\H{o}s-R\'enyi random graph process investigated by Palla, Der\'enyi and Vicsek