We obtained the spectral function of very high quality natural graphite single crystals using angle resolved photoelectron spectroscopy (ARPES). A clear separation of non-bonding and bonding bands and asymmetric lineshape are observed. The asymmetric lineshapes are well accounted for by the finite photoelectron escape depth and the band structure. The extracted width of the spectral function (inverse of the photohole life time) near the K point is, beyond the maximum phonon energy, approximately proportional to the energy as expected from the linear density of states near the Fermi energy. The upper bound for the electron-phonon coupling constant is about 0.2, a much smaller value than the previously reported one.PACS numbers: 74.25.Jb, 63.20.Ls, Recent discoveries of novel physical properties in carbon-based materials such as superconductivity 1,2,3,4,5 and massless Dirac Fermions 6 brought renewed interest in the electronic structure of graphite 7,8 . The peculiarity of the electronic structure of graphite has two aspects: graphite is extremely two dimensional and is a semi-metal. These facts make it fundamentally interesting to study how dimensionality affects the dynamics of the doped carriers and how the carriers in graphite intercalated compounds (GICs) couple to the mediating bosons. In fact, there is a long standing issue in regards to the carrier dynamics in graphite, that is, whether the carriers are Fermi-liquid-like or not. This question motivates experimental studies of electronic structures of these materials by using, for example, angle-resolved photoemission spectroscopy (ARPES) and one can find a long history in the ARPES studies on graphite single crystals 7,8,9,10,11,12,13,14,15 . In addition, studies of graphite-related materials such as single 16 and bilayer graphene 17 and GICs 18,19 can be found.High quality ARPES data from graphite is difficult to obtain despite graphite's two dimensional, inert nature. The problems associated with ARPES experiments on graphite are due mostly to difficulty in proper surface preparation and to some extent to the low quality of the single crystals. For example, the extreme twodimensional nature of graphite inevitably produces small flakes (many are small enough to be seen only under microscopes) on the cleaved surfaces which ruins the momentum resolution in ARPES. Such difficulties prevented one from obtaining good quality data to extract reliable information on the many-body interactions such as electron-phonon coupling (EPC). Therefore, unless such difficulties are overcome, reliable information on manybody interactions can not be extracted from the data. As a result, the experimental data in regards to the electron lifetime have been obtained mostly by time-resolved photoelectron spectroscopy on highly oriented pyrolytic graphite 20,21 .Motivated by the renewed interest in the carrier dynamics in graphite, we have performed ARPES studies on graphite single crystals. Our goal was to extract reliable quantitative information on the EPC from ARPES data. To ...