  Monolayer graphene under a strong perpendicular field exhibit quantum Hall
ferromagnetism with spontaneously broken spin and valley symmetry. The
approximate SU(4) spin/valley symmetry is broken by small lattice scale effects
in the central Landau level corresponding to filling factors $\nu=0,\pm 1$.
Notably the ground state at $\nu=0$ is believed to be a canted
antiferromagnetic (AF) or a ferromagnetic (F) state depending on the component
of the magnetic field parallel to the layer and the strength of small
anisotropies. We study the skyrmions for the filling factors $\nu=\pm 1,0$ by
using exact diagonalizations on the spherical geometry. If we neglect
anisotropies we confirm the validity of the standard skyrmion picture
generalized to four degrees of freedom. For filling factor $\nu=- 1$ the hole
skyrmion is an infinite-size valley skyrmion with full spin polarization
because it does not feel the anisotropies. The electron skyrmion is also always
of infinite size. In the F phase it is always fully polarized while in the AF
phase it undergoes continuous magnetization under increasing Zeeman energy. In
the case of $\nu=0$ the skyrmion is always maximally localized in space both in
F and AF phase. In the F phase it is fully polarized while in the AF it has
also progressive magnetization with Zeeman energy. The magnetization process is
unrelated to the spatial profile of the skyrmions contrary to the SU(2) case.
In all cases the skyrmion physics is dominated by the competition between
anisotropies and Zeeman effect but not directly by the Coulomb interactions,
breaking universal scaling with the ratio Zeeman to Coulomb energy.
