  We investigate the melting phenomena of pristine, free-standing infinite and
finite size graphene sheets via molecular dynamics simulation using AIREBO
potential as implemented in the LAMMPS package. In our simulations, the
temperature of the systems under investigation are systematically heated up
using two independent heating protocols so that the resultant melting
temperatures from both schemes can be checked against each other for
consistency. The melting temperature of infinite graphene sheet is obtained by
following three independent computational experiments. In the first experiment,
we simulate the melting of various finite size graphenes, and then determine
the melting temperature of infinite graphene sheet as the temperature at which
the finite graphenes asymptotically grow in size. In the second experiment, we
simulate the melting of infinite single-wall carbon-nanotubes (SWCNTs) with
different radius, and then determine the melting temperature of infinite
graphene sheet as the temperature at which the radius of SWCNTs asymptotically
grows in size. In the third experiment, we heat up an infinite graphene that is
formed by constructing a rectangular supercell which is subjected to periodic
boundary condition at it sides. Melting temperature for infinite graphene
obtained based on the first approach yields $\sim$ 5799 K $\pm$ 22 K. The
second approach yield $\sim$5302 K $\pm$ 36 K, whereas $\sim$5355 $\pm$ 140 K
from the third. There is an apparent disparity between the results from the
first experiment and that of the second and third experiments due to
differences in the technical details in these MD simulations. We cautiously
conclude that, based on the consistency of the data of the second and third
experiments, that a free-standing infinite graphene sheet melts at the
temperature of 5302 K $\pm$ 36 K, using AIREBO forcefield.
