Order-preserving 1-string representations of planar graphs

Therese Biedl; Martin Derka

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arXiv · 1609.08132

Order-preserving 1-string representations of planar graphs

Therese Biedl·Martin Derka

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Abstract

This paper considers 1-string representations of planar graphs that are order-preserving in the sense that the order of crossings along the curve representing vertex $v$ is the same as the order of edges in the clockwise order around $v$ in the planar embedding. We show that this does not exist for all planar graphs (not even for all planar 3-trees), but show existence for some subclasses of planar partial 3-trees. In particular, for outer-planar graphs it can be order-preserving and outer-string in the sense that all ends of strings are on the outside of the representation.

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BibTeX RIS

Therese Biedl, Martin Derka. 2016-09-26. Order-preserving 1-string representations of planar graphs. https://arxiv.org/abs/1609.08132

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