In order to investigate the existence of carbon in the core, we performed high-pressure melting experiments using a Kawai-type multi-anvil apparatus by two methods: (1) quench experiments up to 14GPa and 2200 degrees C and (2) in situ X-ray diffraction experiments up to 29GPa. From the quench experiments, carbon solubility in molten iron and liquidus phase relations in the Fe-C system was investigated. The carbon solubility in molten iron is 8.5 wt% at 5 GPa and 2000 degrees C, where graphite is the liquidus phase. At 10-14GPa, the carbon solubility in molten iron coexisting with diamond is about 7 wt% at 2000 degrees C and is pressure insensitive. At 5 GPa, Fe(3)C (6.7 wt% C) is the liquidus phase below 1400 degrees C. Above 10 GPa, Fe(7)C(3) (8.4 wt% C) appears as the liquidus phase below 1700 degrees C and Fe(3)C melts incongruently to liquid iron and Fe(7)C(3) at temperatures below 1500 degrees C. From in situ X-ray diffraction observations, the incongruent melting of Fe(3)C was found to occur at least up to 29 GPa, and liquidus temperatures of the Fe(3)C composition were found to be 1825 and 1925 degrees C at 21.0 and 29.2 GPa, respectively. Based on our results, it is concluded that large amount of carbon could be incorporated into the Earth's core if the Earth forming material was rich in carbon. Our result also shows that Fe(7)C(3) Would be the first crystallizing phase from the liquid of the outer core, implying that Fe(7)C(3) could be a potential constituent of the solid inner core. (C) 2008 Elsevier B.V. All rights reserved.