The complexity of computing the cylindrical and the $t$-circle crossing number of a graph
Combinatorics
2019-04-29 v1
Abstract
A plane drawing of a graph is {\em 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 {\em cylindrical crossing number} of a graph is the minimum number of crossings in a cylindrical drawing of . 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 settle this by showing that this problem is NP-complete. Moreover, we show an analogous result for the natural generalization of the cylindrical crossing number, namely the -{\em circle crossing number}.
Keywords
Cite
@article{arxiv.1708.01942,
title = {The complexity of computing the cylindrical and the $t$-circle crossing number of a graph},
author = {Frank Duque and Hernán González-Aguilar and César Hernández-Vélez and Jesús Leaños and Carolina Medina},
journal= {arXiv preprint arXiv:1708.01942},
year = {2019}
}