  The low energy spectrum of a zigzag graphene ribbon contains two gapless
bands with highly non-linear dispersion, $\epsilon(k)=\pm |\pi-k|^W$, where $W$
is the width of the ribbon. The corresponding states are located at the two
opposite zigzag edges. Their presence reflects the fact that the clean ribbon
is a quasi one dimensional system naturally fine-tuned to the topological {\em
multicritical} point. This quantum critical point separates a topologically
trivial phase from the topological one with the index $W$. Here we investigate
the influence of the (chiral) symmetry-preserving disorder on such a
multicritical point. We show that the system harbors delocalized states with
the localization length diverging at zero energy in a manner consistent with
the $W=1$ critical point. The same is true regarding the density of states
(DOS), which exhibits the universal Dyson singularity, despite the clean DOS
being substantially dependent on $W$. On the other hand, the zero-energy
localization length critical exponent, associated with the lattice staggering,
is not universal and depends on the topological index $W$.
