Track Layouts of Graphs

@article{Dujmovic2004TrackLO,
  title={Track Layouts of Graphs},
  author={Vida Dujmovic and Attila P{\'o}r and David R. Wood},
  journal={Discrete Mathematics & Theoretical Computer Science},
  year={2004},
  volume={6},
  pages={497-522}
}
A \emph{$(k,t)$-track layout} of a graph $G$ consists of a (proper) vertex $t$-colouring of $G$, a total order of each vertex colour class, and a (non-proper) edge $k$-colouring such that between each pair of colour classes no two monochromatic edges cross. This structure has recently arisen in the study of three-dimensional graph drawings. This paper presents the beginnings of a theory of track layouts. First we determine the maximum number of edges in a $(k,t)$-track layout, and show how to… CONTINUE READING

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