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arXiv · 1403.1273

Toroidal grid minors and stretch in embedded graphs

Markus Chimani·Petr Hlineny·Gelasio Salazar
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Abstract

We investigate the toroidal expanse of an embedded graph G, that is, the size of the largest toroidal grid contained in G as a minor. In the course of this work we introduce a new embedding density parameter, the stretch of an embedded graph G, and use it to bound the toroidal expanse from above and from below within a constant factor depending only on the genus and the maximum degree. We also show that these parameters are tightly related to the planar crossing number of G. As a consequence of our bounds, we derive an efficient constant factor approximation algorithm for the toroidal expanse and for the crossing number of a surface-embedded graph with bounded maximum degree.

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Markus Chimani, Petr Hlineny, Gelasio Salazar. 2014-03-06. Toroidal grid minors and stretch in embedded graphs. https://arxiv.org/abs/1403.1273

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