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arXiv · 1608.07662

Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time

Seok-Hee Hong·Hiroshi Nagamochi
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Abstract

Thomassen characterized some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph is drawable in straight-lines if and only if it does not contain the configuration [C. Thomassen, Rectilinear drawings of graphs, J. Graph Theory, 10(3), 335-341, 1988]. In this paper, we characterize some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph can be re-embedded into a straight-line drawable 1-plane embedding of the same graph if and only if it does not contain the configuration. Re-embedding of a 1-plane embedding preserves the same set of pairs of crossing edges. We give a linear-time algorithm for finding a straight-line drawable 1-plane re-embedding or the forbidden configuration.

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Seok-Hee Hong, Hiroshi Nagamochi. 2016-08-27. Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time. https://arxiv.org/abs/1608.07662

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