  We present electronic transport measurements through short and narrow (30x30
nm) single layer graphene constrictions on a hexagonal boron nitride substrate.
While the general observation of Coulomb-blockade is compatible with earlier
work, the details are not: we show that the area on which charge is localized
can be significantly larger than the area of the constriction, suggesting that
the localized states responsible for Coulomb-blockade leak out into the
graphene bulk. The high bulk mobility of graphene on hexagonal boron nitride,
however, seems not consistent with the short bulk localization length required
to see Coulomb-blockade. To explain these findings, charge must instead be
primarily localized along the imperfect edges of the devices and extend along
the edge outside of the constriction. In order to better understand the
mechanisms, we compare the experimental findings with tight-binding simulations
of such constrictions with disordered edges. Finally we discuss previous
experiments in the light of these new findings.
