  We show that near an armchair edge of a wide graphene channel, and in the
presence of a smooth step-like electrostatic lateral confining potential, the
chirality, spectrum, spatial structure, and number of the fundamental edge
magnetoplasmons (EMPs), in the $\nu=2$ regime of the quantum Hall effect,
depend strongly on the position of the Fermi level $E_{F}$. (i) When $E_{F}$ is
small enough and intersects four degenerate states of the zero Landau level
(LL) at one location and two degenerate states of this level at a different
one, two fundamental, counter propagating EMPs exist with opposite chirality.
This is in contrast with EMPs in conventional two-dimensional electron systems
in which only one fundamental EMP exists. For the same wave vector these EMPs
have different moduli of phase velocities and an essential spatial overlap.
These EMPs can be on resonance in a wide range of frequencies, for micron or
submicron lengths along the edge. (ii) When $E_{F}$ is sufficiently high and
intersects only two degenerate states of the zero LL only one fundamental EMP
exists with the usual chirality.
