A pair of trees without a simultaneous geometric embedding in the plane

Details A pair of trees without a simultaneous geometric embedding in the plane A pair of trees without a simultaneous geometric embedding in the plane

2005-10-18

arxiv.org/abs/cs/0510053v2

Computer Science

Computational Geometry

This paper has been withdrawn by the author because it had turned out that the result was already known before

Scientific paper

Any planar graph has a crossing-free straight-line drawing in the plane. A simultaneous geometric embedding of two n-vertex graphs is a straight-line drawing of both graphs on a common set of n points, such that the edges withing each individual graph do not cross. We consider simultaneous embeddings of two labeled trees, with predescribed vertex correspondences, and present an instance of such a pair that cannot be embedded. Further we provide an example of a planar graph that cannot be embedded together with a path when vertex correspondences are given.

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