The melting lines of graphite and liquid carbon have been studied for a long time. However, numerous controversies still remain in this field; for instance, different experiments give different melting temperatures. In this work, we explore the melting lines of graphite and graphene by means of classical and ab-initio molecular dynamics. We show that the empirical models developed on the basis of experimental data (AIREBO potential, Tersoff potential and some others) fail to reproduce the properties of liquid carbon properly. The models fitted to ab-initio data (LCBOPII and GAP) give much better results. However, both types of empirical models and ab-initio simulations evidence the presence of smooth structural crossover in liquid carbon. We also show that the “melting” of graphene discussed in previous works on computer simulation is indeed sublimation and propose a novel method to simulate the melting of graphene: simulation of graphene sheet in argon atmosphere. The melting temperature of graphene in argon atmosphere appears to be close to the melting temperature of graphite.