Exact Crossing Number Parameterized by Vertex Cover

Investor logo

Warning

This publication doesn't include Faculty of Education. It includes Faculty of Informatics. Official publication website can be found on muni.cz.
Authors

HLINĚNÝ Petr SANKARAN Abhisekh

Year of publication 2019
Type Article in Proceedings
Conference GD 2019: Graph Drawing and Network Visualization
MU Faculty or unit

Faculty of Informatics

Citation
Web
Doi http://dx.doi.org/10.1007/978-3-030-35802-0_24
Keywords Graph drawing; Crossing number; Parameterized complexity; Vertex cover
Description 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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.