Exact Crossing Number Parameterized by Vertex Cover
Abstract
We prove that the exact crossing number of a graph can be efficiently computed for simple graphs having bounded vertex cover. In more precise words, Crossing Number is in FPT when parameterized by the vertex cover size. This is a notable advance since we know only very few nontrivial examples of graph classes with unbounded and yet efficiently computable crossing number. Our result can be viewed as a strengthening of a previous result of Lokshtanov [arXiv, 2015] that Optimal Linear Arrangement is in FPT when parameterized by the vertex cover size, and we use a similar approach of reducing the problem to a tractable instance of Integer Quadratic Programming as in Lokshtanov's paper.
Cite
@article{arxiv.1906.06048,
title = {Exact Crossing Number Parameterized by Vertex Cover},
author = {Petr Hliněný and Abhisekh Sankaran},
journal= {arXiv preprint arXiv:1906.06048},
year = {2019}
}
Comments
Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019)