  We use driven Monte Carlo dynamics to study the resistive behavior of
superconducting Josephson junction arrays on a honeycomb lattice in a magnetic
field corresponding to $f$ flux quantum per plaquette. While for $f=1/3$ the
onset of zero resistance is found at nonzero temperature, for $f=1/2$ the
results are consistent with a transition scenario where the critical
temperature vanishes and the linear resistivity shows thermally activated
behavior. We determine the thermal critical exponent of the zero-temperature
transition for $f=1/2$, from a dynamic scaling analysis of the nonlinear
resistivity. The resistive behavior agrees with recent results obtained for the
phase-coherence transition from correlation length calculations and with
experimental observations on ultra-thin superconducting films with a triangular
pattern of nanoholes.
