In this thesis we determine necessary and sufficient conditions for the existence of an
equitably ℓ-colourable balanced incomplete block design for any positive integer ℓ > 2.
In particular, we present a method for constructing non-trivial equitably ℓ-colourable
BIBDs and prove that these designs are the only non-trivial equitably ℓ-colourable
BIBDs that exist. We also observe that every equitable ℓ-colouring of a BIBD yields
both an equalised ℓ-colouring and a proper 2-colouring of the same BIBD. We also
discuss generalisations of these concepts including open questions for further research.
The main results presented in this thesis also appear in [7]
