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Almost half of the stellar systems in the solar neighborhood are made up ofmultiple stars. In multiple-star systems, planet formation is under thedynamical influence of stellar companions, and the planet occurrence rate isexpected to be different from that for single stars. There have been numerousstudies on the planet occurrence rate of single star systems. However, to fullyunderstand planet formation, the planet occurrence rate in multiple-starsystems needs to be addressed. In this work, we {{infer}} the planet occurrencerate in multiple-star systems by measuring the stellar multiplicity rate forplanet host stars. For a sub-sample of 56 $Kepler$ planet host stars, we useadaptive optics (AO) imaging and the radial velocity (RV) technique to searchfor stellar companions. The combination of these two techniques results in highsearch completeness for stellar companions. We detect 59 visual stellarcompanions to 25 planet host stars with AO data. {{Three stellar companions arewithin 2$^{\prime\prime}$, and 27 within 6$^{\prime\prime}$. We also detect 2possible stellar companions (KOI 5 and KOI 69) showing long-term RVacceleration.}} After correcting for a bias against planet detection inmultiple-star systems due to flux contamination, we find that planet formationis suppressed in multiple-star systems with separations smaller than 1500 AU.Specifically, we find that compared to single star systems, planets inmultiple-star systems occur $4.5\pm3.2$, $2.6\pm1.0$, and $1.7\pm0.5$ timesless frequently when a stellar companion is present at a distance of 10, 100,and 1000 AU, respectively. This conclusion applies only to circumstellarplanets; the planet occurrence rate for circumbinary planets requires furtherinvestigation.

Influence of Stellar Multiplicity On Planet Formation. II. Planets Are Less Common in Multiple-Star Systems with Separations Smaller than 1500 AU