  At low-energy, the band structure of graphene can be approximated by two
degenerate valleys $(K,K^{\prime})$ about which the electronic spectra of the
valence and conduction bands have linear dispersion relations. An electronic
state in this band spectrum is a linear superposition of states from the $A$
and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing
magnetic field, the band spectrum is split into Landau levels with level N=0
having zero weight on the $B(A)$ sublattice for the $% K(K^{\prime})$ valley.
Treating the valley index as a pseudospin and assuming the real spins to be
fully polarized, we compute the energy of Wigner and Skyrme crystals in the
Hartree-Fock approximation. We show that Skyrme crystals have lower energy than
Wigner crystals \textit{i.e.} crystals with no pseudospin texture in some range
of filling factor $\nu $ around integer fillings. The collective mode spectrum
of the valley-skyrmion crystal has three linearly-dispersing Goldstone modes in
addition to the usual phonon mode while a Wigner crystal has only one extra
Goldstone mode with a quadratic dispersion. We comment on how these modes
should be affected by disorder and how, in principle, a microwave absorption
experiment could distinguish between Wigner and Skyrme crystals.
