Young, Kailyn M.2011-05-022011-05-0220112011-05-02http://hdl.handle.net/1828/3277A 2-dipath k-colouring of an oriented graph G is an assignment of k colours, 1,2, . . . , k, to the vertices of G such that vertices joined by a directed path of length two are assigned different colours. The 2-dipath chromatic number is the minimum number of colours needed in such a colouring. There are two possible models, depending on whether adjacent vertices must also be assigned different colours. For both models of 2-dipath colouring we develop the basic theory, including characterizing the oriented graphs that can be 2-dipath coloured using a small number of colours, finding bounds on the 2-dipath chromatic number, determining the complexity of deciding the existence of a 2-dipath k-colouring, describing a homomorphism model, and showing how to determine the 2-dipath chromatic number of tournaments and bipartite tournaments.engraph theoryoriented graphstournamentsThesisAvailable to the World Wide Web