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arXiv · 1906.06048

Exact Crossing Number Parameterized by Vertex Cover

Petr Hliněný·Abhisekh Sankaran
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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.

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Petr Hliněný, Abhisekh Sankaran. 2019-06-14. Exact Crossing Number Parameterized by Vertex Cover. https://arxiv.org/abs/1906.06048

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