  We study the competition between the electron liquid and solid phases, such
as Wigner crystal and bubbles, in partially filled Landau levels (LLs) of
multilayer graphene. Graphene systems offer a versatile platform for
controlling band dispersion by varying the number of its stacked layers. The
band dispersion determines the LL wave functions, and consequently, the
LL-projected Coulomb interaction in graphene and its multilayers is different
from that in conventional semiconductors like GaAs. As a result, the energies
of the liquid and solid phases are different in the different LLs of multilayer
graphene, leading to an alternative phase diagram for the stability of these
phases, which we work out. The phase diagram of competing solid and liquid
phases in the LLs of monolayer graphene has been studied previously. Here, we
primarily consider $AB{-}$ or Bernal$-$stacked bilayer graphene (BLG) and
$ABC{-}$stacked trilayer graphene (TLG) and focus on the Laughlin fractions. We
determine the cohesive energy of the solid phase using the Hartree-Fock
approximation, and the energy of the Laughlin liquid is computed analytically
via the plasma sum rules. We find that at the Laughlin fillings, the electron
liquid phase has the lowest energy among the phases considered in the
$\mathcal{N}{=}0, 1, 2$ LLs of BLG, as well as in the $\mathcal{N}{=}3, 4$ LLs
of TLG, while in the $\mathcal{N}{>}2$ LLs of BLG and $\mathcal{N}{>}4$ LLs of
TLG, the solid phases are more favorable. We also discuss the effect of
impurities on the above-mentioned phase diagram.
