  Using the redMaPPer cluster catalogue based on the Sloan Digital Sky Survey
(SDSS) photometry, we investigate the importance of major mergers in the
stellar mass build-up of brightest cluster galaxies (BCGs) between $0.08 \leq z
\leq 0.50$. We use the SDSS spectroscopy, supplemented with spectroscopic
observations from the Southern African Large Telescope at higher redshifts, to
identify which BCGs and nearby companions are potential major merger
candidates. We use the pair fraction as a proxy for the merger fraction in
order to determine how much stellar mass growth the BCGs have experienced due
to major mergers. We observe a weak trend of the BCG pair fraction increasing
with decreasing redshift, suggesting that major mergers may become more
important towards the present day. Major mergers are found to contribute, on
average, $24 \pm 14 $ $(29 \pm 17)$ per cent towards the stellar mass of a
present day BCG since $z=0.32$ (0.45), assuming that half of the companion's
stellar mass is accreted onto the BCG. Furthermore, using our merger results in
conjunction with predictions from two recent semi-analytical models along with
observational measurements from the literature, we find that major mergers have
sufficient stellar material to account for the stellar mass growth of the
intracluster light between $z=0.3$ and $z=0$.
