Absolute magnitude plotted vs. redshift for 10,000 galaxies selected at random from our SDSS spectroscopic catalog of about 337,000 galaxies. The dashed black lines enclose all potential companion galaxies; galaxies within this region have ﹩14.5< m_{r}< 17.5﹩. The solid red lines enclose all potential host galaxies; galaxies within this region differ by at least 0.753 mag from the dashed lines. For these potential host galaxies, all companions within a luminosity ratio of 1:2 are therefore detectable.