  The Bose-Einstein condensation (BEC) of magnetoexcitonic polaritons in
two-dimensional (2D) electron-hole system embedded in a semiconductor
microcavity in a high magnetic field $B$ is predicted. There are two physical
realizations of 2D electron-hole system under consideration: a graphene layer
and quantum well (QW). A 2D gas of magnetoexcitonic polaritons is considered in
a planar harmonic potential trap. Two possible physical realizations of this
trapping potential are assumed: inhomogeneous local stress or harmonic electric
field potential applied to excitons and a parabolic shape of the semiconductor
cavity causing the trapping of microcavity photons. The effective Hamiltonian
of the ideal gas of cavity polaritons in a QW and graphene in a high magnetic
field and the BEC temperature as functions of magnetic field are obtained. It
is shown that the effective polariton mass $M_{\rm eff}$ increases with
magnetic field as $B^{1/2}$. The BEC critical temperature $T_{c}^{(0)}$
decreases as $B^{-1/4}$ and increases with the spring constant of the parabolic
trap. The Rabi splitting related to the creation of a magnetoexciton in a high
magnetic field in graphene and QW is obtained. It is shown that Rabi splitting
in graphene can be controlled by the external magnetic field since it is
proportional to $B^{-1/4}$, while in a QW the Rabi splitting does not depend on
the magnetic field when it is strong.
