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arXiv · 2509.03121

Expansion of gap-planar graphs

David R. Wood
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Abstract

A graph is $k$-gap-planar if it has a drawing in the plane such that every crossing can be charged to one of the two edges involved so that at most $k$ crossings are charged to each edge. We show this class of graphs has linear expansion. In particular, every $r$-shallow minor of a $k$-gap-planar graph has density $O(rk)$. Several extensions of this result are proved: for topological minors, for $k$-cover-planar graphs, for $k$-gap-cover-planar graphs, and for drawings on any surface. Application to graph colouring are presented.

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David R. Wood. 2025-10-17. Expansion of gap-planar graphs. https://arxiv.org/abs/2509.03121

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