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.
CITATION STYLE
Biedl, T., & Derka, M. (2017). Order-preserving 1-string representations of planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10139 LNCS, pp. 283–294). Springer Verlag. https://doi.org/10.1007/978-3-319-51963-0_22
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