  We investigate bond percolation on the non-planar Hanoi network (HN-NP),
which was studied in [Boettcher et al. Phys. Rev. E 80 (2009) 041115]. We
calculate the fractal exponent of a subgraph of the HN-NP, which gives a lower
bound for the fractal exponent of the original graph. This lower bound leads to
the conclusion that the original system does not have a non-percolating phase,
where only finite size clusters exist, for p>0, or equivalently, that the
system exhibits either the critical phase, where infinitely many infinite
clusters exist, or the percolating phase, where a unique giant component
exists. Monte Carlo simulations support our conjecture.
