  Close binary central stars of planetary nebulae (PNe) must have formed
through a common envelope evolution during the giant phase experienced by one
of the stars. Transfer of the angular momentum from the binary system to the
envelope leads to the shortening of the binary separations from the radius of
red giant to the radius of the order of few tenths of AU. Thus, close binary
central stars of planetary nebulae are laboratories to study the common
envelope phase of evolution. The close binary fraction in the Galaxy has been
measured in various sky surveys, but the close binary fraction is not yet well
constrained for the Magellanic Clouds, and our results may help the study of
common envelope evolution in low-metallicity environments. This paper presents
a continuation of our study of variability in the Magellanic Cloud planetary
nebulae on the basis of data from the OGLE survey. Previously, we had analysed
the OGLE data in the Small Magellanic Cloud. Here, the study is extended to the
Large Magellanic Cloud (LMC). In this paper we search for close binary central
stars with the aim to constrain the binary fraction and period distribution in
the LMC. We identified 290 counterparts of PNe in the LMC in the I-band images
from the OGLE-III and OGLE-IV surveys. However, the light curves of ten objects
were not accessible in the OGLE database, and thus we analysed the time series
photometry of 280 PNe. In total, 32 variables were found, but 5 of them turned
out to be foreground objects. Another 18 objects show irregular or regular
variability that is not attributable to the binarity of their central stars.
Their status and the nature of their variability will be verified in the
follow-up paper. Nine binary central stars of PNe with periods between 0.24 and
23.6 days were discovered. The obtained fraction for the LMC PNe is
3.3^(+2.6)_(-1.6)% without correcting for incompleteness.
