  We present a theoretical study of flat-band superconductivity for fully
spin-polarized triplet pairing with $p$-wave symmetry. We consider the effect
of disorder and calculate the disorder-averaged Green's functions
diagrammatically in first-order Born approximation. In the clean limit, we find
that, similarly to the case of $s$-wave pairing in a flat-band, both the gap
and the critical temperature depend linearly on the attractive interaction
strength. We derive the critical-temperature suppression formula for the
flat-band case and find that $p$-wave flat-band superconductivity is more
robust than the standard case of a band with finite density of states,
particularly in more disordered samples.
