On the oriented chromatic number of dense graphs

  title={On the oriented chromatic number of dense graphs},
  author={David R. Wood},
  journal={Contributions to Discrete Mathematics},
  • David R. Wood
  • Published 2007 in Contributions to Discrete Mathematics
Let G be a graph with n vertices, m edges, average degree d, and maximum degree ∆. The oriented chromatic number of G is the maximum, taken over all orientations of G, of the minimum number of colours in a proper vertex colouring such that between every pair of colour classes all edges have the same orientation. We investigate the oriented chromatic number of graphs, such as the hypercube, for which d ≥ log n. We prove that every such graph has oriented chromatic number at least Ω( √ n). In the… CONTINUE READING