  The Super-Kamiokande detector can be used to search for neutrinos in time
coincidence with gravitational waves detected by the LIGO-Virgo Collaboration
(LVC). Both low-energy ($7-100$ MeV) and high-energy ($0.1-10^5$ GeV) samples
were analyzed in order to cover a very wide neutrino spectrum. Follow-ups of 36
(out of 39) gravitational waves reported in the GWTC-2 catalog were examined;
no significant excess above the background was observed, with 10 (24) observed
neutrinos compared with 4.8 (25.0) expected events in the high-energy
(low-energy) samples. A statistical approach was used to compute the
significance of potential coincidences. For each observation, p-values were
estimated using neutrino direction and LVC sky map ; the most significant event
(GW190602_175927) is associated with a post-trial p-value of $7.8\%$
($1.4\sigma$). Additionally, flux limits were computed independently for each
sample and by combining the samples. The energy emitted as neutrinos by the
identified gravitational wave sources was constrained, both for given flavors
and for all-flavors assuming equipartition between the different flavors,
independently for each trigger and by combining sources of the same nature.
