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

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arxiv 1908.05706 v2 pith:5UHWWFGX submitted 2019-08-15 cs.CG cs.DS

Therese Biedl , Erin Wolf Chambers , David Eppstein , Arnaud De Mesmay , Tim Ophelders This is my paper · ORCID
classification cs.CGcs.DS
keywords heightboundsdrawinggraphgrid-majorhomotopylowerother
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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.

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  1. Excluding a rectangular grid

    math.CO 2025-01 conditional novelty 8.0 of 10

    A new parameter family, k-treedepth, is characterized by excluded minors T□P_l for all k-vertex trees T, unifying treedepth, the ladder theorem, and the Grid-Minor Theorem.

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