  It has been suggested that ultrahigh energy neutrinos can acquire
cross-sections approaching hadronic size if the string scale is as low as 1-10
TeV. In this case, the vertical air showers observed with energies above the
Greisen-Zatsepin-Kuzmin cutoff at E approximately 6x10^{19} eV could be
initiated by neutrinos which are the only known primaries able to travel long
distances unimpeded. We have calculated the neutrino-nucleon cross-section due
to the exchange of Kaluza-Klein excitations of the graviton in a field
theoretical framework. We have found that the neutrino-nucleon cross section
and the transferred energy per interaction are too small to explain vertical
showers even in the most optimistic scenario.
