Optical Photometric Variable Stars towards the Galactic \hii region NGC
  2282
  We report here CCD $I$-band time-series photometry of a young (2$-$5 Myr)
cluster NGC 2282 to identify and understand the variability of
pre-main-sequence (PMS) stars. The $I$-band photometry, down to $\sim$ 20.5
mag, enables us to probe the variability towards the lower mass end ($\sim$ 0.1
M$_\odot$) of the PMS stars. From the light curves of 1627 stars, we identified
62 new photometric variable candidates. Their association with the region was
established from H$\alpha$ emission and infrared (IR) excess. Among 62
variables, 30 young variables exhibit H$\alpha$ emission, near-IR (NIR)/mid-IR
(MIR) excess or both, and they are candidate members of the cluster. Out of 62
variables, 41 are periodic variables with the rotation rate ranging from 0.2 to
7 days. The period distribution exhibits a median period at $\sim$ 1-day as in
many young clusters (e.g., NGC~2264, ONC, etc.), but it follows a uni-modal
distribution unlike others having bimodality with the slow rotators peaking at
$\sim$ 6$-$8 days. To investigate the rotation-disk and variability-disk
connection, we derived NIR excess from $\Delta$(I$-$K) and MIR excess from
$Spitzer$ [3.6]$-$[4.5] $\mu$m data. No conclusive evidence of slow rotation
with the presence of disks around stars and fast rotation for diskless stars is
obtained from our periodic variables. A clear increasing trend of the
variability amplitude with the IR excess is found for all variables.
