  The Galactic centre hosts a crowded, dense nuclear star cluster with a
half-light radius of 4 pc. Most of the stars in the Galactic centre are cool
late-type stars, but there are also >100 hot early-type stars in the central
parsec of the Milky Way. These stars are only 3-8 Myr old. Our knowledge of the
number and distribution of early-type stars in the Galactic centre is
incomplete. Only a few spectroscopic observations have been made beyond a
projected distance of 0.5 pc of the Galactic centre. The distribution and
kinematics of early-type stars are essential to understand the formation and
growth of the nuclear star cluster. We cover the central >4pc^2 of the Galactic
centre using the integral-field spectrograph KMOS. We extracted more than 1,000
spectra from individual stars and identified early-type stars based on their
spectra. Our data set contains 114 bright early-type stars: 6 have narrow
emission lines, 23 are Wolf-Rayet stars, 9 stars have featureless spectra, and
76 are O/B type stars. Our wide-field spectroscopic data confirm that the
distribution of young stars is compact, with 90% of the young stars identified
within 0.5 pc of the nucleus. We identify 24 new O/B stars primarily at large
radii. We estimate photometric masses of the O/B stars and show that the total
mass in the young population is >12,000M_sun. The O/B stars all appear to be
bound to the Milky Way nuclear star cluster, while less than 30% belong to the
clockwise rotating disk. The central concentration of the early-type stars is a
strong argument that they have formed in situ. A large part of the young O/B
stars is not on the disk, which either means that the early-type stars did not
all form on the same disk or that the disk is dissolving rapidly. [abridged]
