  The KM3NeT neutrino telescope is currently being deployed at two different
sites in the Mediterranean Sea. First searches for astrophysical neutrinos have
been performed using data taken with the partial detector configuration already
in operation. The paper presents the results of two independent searches for
neutrinos from compact binary mergers detected during the third observing run
of the LIGO and Virgo gravitational wave interferometers. The first search
looks for a global increase in the detector counting rates that could be
associated with inverse beta decay events generated by MeV-scale electron
anti-neutrinos. The second one focuses on upgoing track-like events mainly
induced by muon (anti-)neutrinos in the GeV--TeV energy range. Both searches
yield no significant excess for the sources in the gravitational wave catalogs.
For each source, upper limits on the neutrino flux and on the total energy
emitted in neutrinos in the respective energy ranges have been set. Stacking
analyses of binary black hole mergers and neutron star-black hole mergers have
also been performed to constrain the characteristic neutrino emission from
these categories.
