  Graphene, a hexagonal sheet of $sp^2$-bonded carbon atoms, has extraordinary
properties which hold immense promise for future nanoelectronic applications.
Unfortunately, the popular preparation methods of micromechanical cleavage and
chemical exfoliation of graphite do not easily scale up for application
purposes. Epitaxial graphene provides an attractive alternative, though there
are many challenges, not least of which is the absence of an understanding of
the complex atomistic assembly kinetics of graphene. Here, we present a simple
rate theory of epitaxial graphene growth on close-packed metal surfaces. Based
on recent low-energy electron-diffraction microscopy experiments (LEEM)
\cite{loginova09}, our theory supposes that graphene islands grow predominantly
by the addition of five-atom clusters, rather than solely by the capture of
diffusing carbon atoms. With suitably chosen kinetic parameters, our theory
produces a time-dependent carbon adatom density that is in quantitative
agreement with measured data. The temperature-dependence of this adatom density
at the onset of nucleation leads us to predict that the smallest stable
precursor to graphene growth is an immobile island composed of six five-atom
clusters. Our findings provide a starting point for more detailed simulations
which will yield important input to developing strategies for the large-scale
production of epitaxial graphene.
