| Full text | |
| Author(s): |
Duque, Frank
[1]
;
Gonzalez-Aguilar, Hernan
[2]
;
Hernadez-Velez, Cesar
[2]
;
Leanos, Jesus
[3]
;
Medina, Carolina
[4]
Total Authors: 5
|
| Affiliation: | [1] Univ Antioquia, Inst Matemat, Medellin 050010 - Colombia
[2] Univ Autonoma San Luis Potosi, Fac Ciencias, San Luis Potosi 78290 - Mexico
[3] Univ Autonoma Zacatecas, Unidad Acad Matemat, Zacatecas 9800 - Mexico
[4] Univ Autonoma San Luis Potosi, Inst Fis, San Luis Potosi 78290 - Mexico
Total Affiliations: 4
|
| Document type: | Journal article |
| Source: | ELECTRONIC JOURNAL OF COMBINATORICS; v. 25, n. 2 JUN 8 2018. |
| Web of Science Citations: | 1 |
| Abstract | |
A plane drawing of a graph is cylindrical if there exist two concentric circles that contain all the vertices of the graph, and no edge intersects (other than at its endpoints) any of these circles. The cylindrical crossing number of a graph G is the minimum number of crossings in a cylindrical drawing of G. In his influential survey on the variants of the definition of the crossing number of a graph, Schaefer lists the complexity of computing the cylindrical crossing number of a graph as an open question. In this paper, we prove that the problem of deciding whether a given graph admits a cylindrical embedding is NP-complete, and as a consequence we show that the t-cylindrical crossing number problem is also NP-complete. Moreover, we show an analogous result for the natural generalization of the cylindrical crossing number, namely the t-circle crossing number. (AU) | |
| FAPESP's process: | 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science |
| Grantee: | Carlos Eduardo Ferreira |
| Support Opportunities: | Research Projects - Thematic Grants |