  This paper presents the results of different searches for correlations
between very high-energy neutrino candidates detected by IceCube and the
highest-energy cosmic rays measured by the Pierre Auger Observatory and the
Telescope Array. We first consider samples of cascade neutrino events and of
high-energy neutrino-induced muon tracks, which provided evidence for a
neutrino flux of astrophysical origin, and study their cross-correlation with
the ultrahigh-energy cosmic ray (UHECR) samples as a function of angular
separation. We also study their possible directional correlations using a
likelihood method stacking the neutrino arrival directions and adopting
different assumptions on the size of the UHECR magnetic deflections. Finally,
we perform another likelihood analysis stacking the UHECR directions and using
a sample of through-going muon tracks optimized for neutrino point-source
searches with sub-degree angular resolution. No indications of correlations at
discovery level are obtained for any of the searches performed. The smallest of
the p-values comes from the search for correlation between UHECRs with IceCube
high-energy cascades, a result that should continue to be monitored.
