  From the scattering of semicoherent-state wavepackets at high magnetic field,
we derive analytically the transmission coefficient of electrons in graphene in
the quantum Hall regime through a smooth constriction described by a quadratic
saddle-point electrostatic potential. We find anomalous half-quantized
conductance steps that are rounded by a backscattering amplitude related to the
curvature of the potential. Furthermore, the conductance in graphene breaks
particle-hole symmetry in cases where the saddle-point potential is itself
asymmetric in space. These results have implications both for the
interpretation of split-gate transport experiments, and for the derivation of
quantum percolation models for graphene.
