The melting point of graphite ranges between 4000 and 5000 K depending on the pressure. The covalent bonds between the individual atoms are very strong. In order for graphite to melt, it is these bonds that need to be broken. The strength of these bonds is comparable to those in diamond, another allotrope of carbon. And similar to diamond, the melting point of graphite would have to be very high. In fact, at normal atmospheric temperature, neither substance can melt. Instead, they burn (or sublimate) at about 3600°C.
However, by increasing the pressure on graphite, it can be induced to melt rather than burn at a high temperature. Experiments have revealed that, depending on the pressure, the melting point of graphite can range between 4000K and 5000K.