Toroidal grid minors and stretch in embedded graphs
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | JOURNAL OF COMBINATORIAL THEORY SERIES B |
| MU Faculty or unit | |
| Citation | |
| Web | http://arxiv.org/abs/1403.1273 |
| Doi | http://dx.doi.org/10.1016/j.jctb.2019.05.009 |
| Keywords | Graph embeddings; Compact surfaces; Edge-width; Toroidal grid; Crossing number; Stretch |
| Description | 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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