A problem of the cosmological evolution of the IGM is recalled and a necessity to find distant (z>0.5) giant radio galaxies (GRGs) with the lobe energy densities lower than about 10^{-14} J m^{-3} to solve this problem is emphasized. Therefore we undertake a search for such GRGs on the southern sky hemisphere using the SALT. In this paper we present a selected sample of the GRG candidates and the first deep detections of distant host galaxies, as well as the low-resolution spectra of the galaxies identified on the DSS frames. The data collected during the Performance Verification (P-V) phase show that 21 of 35 galaxies with the spectroscopic redshift have the projected linear size greater than 1 Mpc (for H_{0}=71 kmsMpc). However their redshifts do not exceed the value of 0.4 and the energy density in only two of them is less than 10^{-14} J m^{-3}. A photometric redshift estimate of one of them (J1420-0545) suggests a linear extent larger than 4.8 Mpc, i.e. a larger than that of 3C236, the largest GRG known up to now.
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