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We study numerically the interplay of phase coherence and vortex-glass statein two-dimensional Josephson-junction arrays with average rational values offlux quantum per plaquette $f$ and random dilution of junctions. For $f=1/2$,we find evidence of a phase coherence threshold value $x_s$, below thepercolation concentration of diluted junctions $x_p$, where the superconductingtransition vanishes. For $x_s < x < x_p$ the array behaves as azero-temperature vortex glass with nonzero linear resistance at finitetemperatures. The zero-temperature critical currents are insensitive tovariations in $f$ in the vortex glass region while they are strongly $f$dependent in the phase coherent region.Comment: 6 pages, 4 figures, to appear in Phys. Rev.

Phase-coherence threshold and vortex-glass state in diluted Josephson-junction arrays in a magnetic field