Expansion of gap-planar graphs
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915560783085568 |
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| author | Wood, David R. |
| author_facet | Wood, David R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Expansion of gap-planar graphs Wood, David R. Combinatorics Discrete Mathematics 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. |
| title | Expansion of gap-planar graphs |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2509.03121 |