List Colourings and Tightness of 4 Colour Theorem

The four colour theorem states every planar graph can be coloured using at most 4 colours. Most mathematicians are unsatisfied with Appel and Haken's proof. List-colouring and the choosability of graphs were introduced in an attempt to prove the four-colour theorem. I introduce some generalizations of choosable colourings as well as open problems.