  A long-standing conjecture of Zsolt Tuza asserts that the triangle covering
number $\tau(G)$ is at most twice the triangle packing number $\nu(G)$, where
the triangle packing number $\nu(G)$ is the maximum size of a set of
edge-disjoint triangles in $G$ and the triangle covering number $\tau(G)$ is
the minimal size of a set of edges intersecting all triangles. In this paper,
we prove that Tuza's conjecture holds in the Erd\H{o}s-R\'enyi random graph
$G(n,m)$ for all range of $m$, closing the gap in what was previously known.
(Recently, this result was also independently proved by Jeff Kahn and Jinyoung
Park.) We employ a random greedy process called the online triangle packing
process to produce a triangle packing in $G(n,m)$ and analyze this process by
using the differential equations method.
