A note on perfect Lucky k-colourable graphs

This paper presents the notion of perfect Lucky k-colouring. Basic conditions for a perfect Lucky k-colourable graph are presented. Application thereof is then presented by obtaining the Lucky 4-polynomials for all connected graphs G on six vertices with ten edges. The chromatic number of these connected graphs is chi(G) = 3 or 4. For k = max{chi(G) : 3 or 4 } = 4, it is possible to find Lucky 4-polynomials for all graphs on six vertices and ten edges. The methodology improves substantially on the fundamental methodology such that, vertex partitions begin with Lucky partition forms immediately. Finally, further problems for research related to this study are presented.