  We explore the multiplicity of exoplanet host stars with high-resolution
images obtained with VLT/SPHERE. Two different samples of systems were
observed: one containing low-eccentricity outer planets, and the other
containing high-eccentricity outer planets. We find that 10 out of 34 stars in
the high-eccentricity systems are members of a binary, while the proportion is
3 out of 27 for circular systems. Eccentric-exoplanet hosts are, therefore,
significantly more likely to have a stellar companion than circular-exoplanet
hosts. The median magnitude contrast over the 68 data sets is 11.26 and 9.25,
in H and K, respectively, at 0.30 arcsec. The derived detection limits reveal
that binaries with separations of less than 50au are rarer for exoplanet hosts
than for field stars. Our results also imply that the majority of
high-eccentricity planets are not embedded in multiple stellar systems (24 out
of 34), since our detection limits exclude the presence of a stellar companion.
We detect the low-mass stellar companions of HD 7449 and HD 211847, both
members of our high-eccentricity sample. HD 7449B was already detected by
Rodigas et al (2016) and our independent observation is in agreement with this
earlier work. HD 211847's substellar companion, previously detected by the
radial velocity method, is actually a low-mass star seen face-on. The role of
stellar multiplicity in shaping planetary systems is confirmed by this work,
although it does not appear as the only source of dynamical excitation.
