Homotopy height, grid-major height and graph-drawing height
arXiv:1908.05706
Abstract
It is well-known that both the pathwidth and the outer-planarity of a graph can be used to obtain lower bounds on the height of a planar straight-line drawing of a graph. But both bounds fall short for some graphs. In this paper, we consider two other parameters, the (simple) homotopy height and the (simple) grid-major height. We discuss the relationship between them and to the other parameters, and argue that they give lower bounds on the straight-line drawing height that are never worse than the ones obtained from pathwidth and outer-planarity.
28 pages, 11 figures. Expanded version of a paper in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019); for the proceedings version, see version 1