Track Layouts of Graphs

A (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. Our focus is on methods for the manipulation of track layouts, and the relationship between track layouts and other models of graph layout, namely stack and queue layouts, and geometric thickness. In addition we determine the maximum number of edges in a (k, t)-track layout, and show how to colour the edges given fixed linear orderings of the vertex colour classes.

• Type: Journal
• Year: 2004
• Where: CORR
• Authors: Vida Dujmovic, Attila Pór, David R. Wood
• Keywords: Colour Classes, CORR 2004, Education, Three-dimensional Graph Drawings, Track Layouts