  A search for a correlation between the luminosities of the brightest stars
and luminosities of their host galaxies was carried out on archived Hubble
Space Telescope (HST) F606W or F555W (V) and F814W (I) images of about 150
nearby galaxies. The sample contains only galaxies with on-going star formation
(SF) and with known distances we derived with the TRGB-method. We correlated
the average absolute luminosities of the three brightest blue and the three
brightest red stars with the luminosity of a host. We found a linear relation
for both the blue and the red stars in irregular and low-mass spiral galaxies.
Their scatters are sufficiently small (0.m4) to make this relations useful for
distance determination for low-mass galaxies. We found that all 31 dwarf
galaxies (M_B>-13m) in our sample lack bright stars (M_V(BS)< -7.m0), probably
due to the physical conditions that prevent their birth. For galaxies with
higher luminosity in the range -18m<M_B<-13m, there is an asymmetry in the
distribution of the number of galaxies relative to the linear dependence,
indicating an increase in the fraction of galaxies with bright stars.
