# Homotopy height, grid-major height and graph-drawing height

## TL;DR

This paper explores two graph parameters, homotopy height and grid-major height, demonstrating they provide better lower bounds on the height of planar straight-line drawings than traditional parameters like pathwidth and outer-planarity.

## Contribution

It introduces and analyzes the relationship of homotopy height and grid-major height, showing they offer improved lower bounds for graph drawing height.

## Key findings

- Homotopy height and grid-major height are related to each other and to existing parameters.
- These parameters provide lower bounds on drawing height that outperform pathwidth and outer-planarity in some cases.
- The paper establishes theoretical relationships between these parameters and graph drawing constraints.

## 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.