2-dipath and proper 2-dipath k-colourings
Date
2011-05-02
Authors
Young, Kailyn M.
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Abstract
A 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.
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Keywords
graph theory, oriented graphs, tournaments