Context :

Aims : The aim of this paper is to discuss the nature of two Type Ic supernovae SN 2007bg and SN 2007bi and their host galaxies .
Both supernovae were discovered in wide-field , non-targeted surveys and are found to be associated with sub-luminous blue dwarf galaxies identified in SDSS images .

Methods : We present BVRI photometry and optical spectroscopy of SN 2007bg and SN 2007bi and their host galaxies .
Their lightcurves and spectra are compared to those of other Type Ic SNe and analysis of these data provides estimates of the energetics , total ejected masses and synthesised mass of ^ { 56 } Ni .
Detection of the host galaxy emission lines allows for metallicity measurements .

Results : Neither SNe 2007bg nor 2007bi were found in association with an observed GRB , but from estimates of the metallicities of their host-galaxies they are found to inhabit similar low-metallicity environments as GRB associated supernovae .
The radio-bright SN 2007bg is hosted by an extremely sub-luminous galaxy of magnitude M _ { B } = -12.4 \pm 0.6 mag and an estimated oxygen abundance of 12 + \log ( { O / H } ) = 8.18 \pm 0.17 ( on the scale ) .
The early lightcurve evolution of SN 2007bg matches the fast-pace decline of SN 1994I giving it one of the fastest post-maximum decline rates of all broad-lined Type Ic supernovae known to date and , when combined with its high expansion velocities , a high kinetic energy to ejected mass ratio ( E _ { K } / M _ { ej } \sim 2.7 ) .
We also show that SN 2007bi is possibly the most luminous Type Ic known , reaching a peak magnitude of M _ { R } \sim - 21.3 mag and displays a remarkably slow decline , following the radioactive decay rate of ^ { 56 } Co to ^ { 56 } Fe throughout the course of its observed lifetime .
SN 2007bi also displays an extreme longevity in its spectral evolution and is still not fully nebular at approximately one year post-maximum brightness .
From a simple model of the bolometric light curve of SN 2007bi we estimate a total ejected ^ { 56 } Ni mass of M _ { Ni } = 3.5 - 4.5 { M } _ { \odot } , the largest ^ { 56 } Ni mass measured in the ejecta of a supernova to date .
There are two models that could explain the high luminosity and large ejected ^ { 56 } Ni mass .
One is a pair-instability supernova ( PISN ) which has been predicted to occur for massive stars at low metallicities .
We measure the host galaxy metallicity of SN 2007bi to be 12 + \log ( { O / H } ) = 8.15 \pm 0.15 ( on the scale ) which is somewhat high to be consistent with the PISN model .
An alternative is the core-collapse of a C+O star of 20 - 40 M _ { \odot } which is the core of a star of originally 50 - 100 M _ { \odot } .

Conclusions :