  We study a geometrically frustrated triangular Ising antiferromagnet in an
external magnetic field which is selectively diluted with nonmagnetic
impurities employing an effective-field theory with correlations and Monte
Carlo simulations. We focus on the frustration-relieving effects of such a
selective dilution on the phase diagram and find that it can lead to rather
intricate phase diagrams in the dilution-field parameters space. In particular,
in a highly (weakly) diluted system the frustration is greatly (little)
relieved and such a system is found to display only the second(first)-order
phase transitions at any field. On the other hand, for a wide interval of
intermediate dilution values the transition remains second order at low fields
but it changes to first order at higher fields and the system displays a
tricritical behavior. The existence of the first-order transition in the region
of intermediate dilution and high fields is verified by Monte Carlo
simulations.
