The generalized graph colouring problem (GCOL) for a fixed integer k, and fixed classes of graphs P1, . . . ,Pk (usually describing some common graph properties), is to decide, for a given graph G, whether the vertex set of G can be partitioned into sets V1, . . . , Vk such that, for each i, the induced subgraph of G on Vi belongs to Pi. It can be seen that GCOL generalizes many natural colouring and partitioning problems on graphs. In this thesis, we focus on generalized colouring problems in… CONTINUE READING