  We present an approach to the melting of graphene based on nucleation theory
for a first order phase transition from the 2D solid to the 3D liquid via an
intermediate quasi-2D liquid.
  The applicability of nucleation theory, supported by the results of
systematic atomistic Monte Carlo simulations, provides an intrinsic definition
of the melting temperature of graphene, $ T_m $, and allows us to determine it.
We find $T_m \simeq 4510$ K, about 250 K higher than that of graphite using the
same interatomic interaction model. The found melting temperature is shown to
be in good agreement with the asymptotic results of melting simulations for
finite disks and ribbons of graphene. Our results strongly suggest that
graphene is the most refractory of all known materials.

Mesoscale and Nanoscale Physics