  The nature of possible evolutionary pathways between various types of dwarf
galaxies is still not fully understood. Blue compact dwarf galaxies (BCDs)
provide a unique window into dwarf galaxy formation and evolution and are often
thought of as an evolutionary stage between different classes of dwarf
galaxies. In this study we use deep optical and near-infrared observations of
the underlying hosts of BCDs in order to study the structural differences
between different types of dwarf galaxies. When compared with dwarf irregular
galaxies of similar luminosities, we find that the underlying hosts of BCDs
have significantly more concentrated light distributions, with smaller scale
lengths and brighter central surface brightnesses. We demonstrate here that the
underlying hosts of BCDs are distinct from the broad continuum of typical dwarf
irregular galaxies, and that it is unlikely that most dwarf irregular galaxies
can transform into a BCD or vice versa. Furthermore, we find that the starburst
in a BCD only brightens it on average by ~0.8 mag (factor of two), in agreement
with other studies. It appears that a BCD is a long-lived and distinct type of
dwarf galaxy that exhibits an exceptionally concentrated matter distribution.
We suggest that it is this compact mass distribution that enables the strong
star formation events that characterize this class of dwarf galaxy, that the
compactness of the underlying host can be used as a distinguishing parameter
between BCDs and other dwarf galaxies, and that it can also be used to identify
BCDs which are not currently experiencing an intense starburst event.
