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Exact Crossing Number Parameterized by Vertex Cover

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HLINĚNÝ Petr SANKARAN Abhisekh

Rok publikování 2019
Druh Článek ve sborníku
Konference GD 2019: Graph Drawing and Network Visualization
Fakulta / Pracoviště MU

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Citace
www http://arxiv.org/abs/1906.06048
Doi http://dx.doi.org/10.1007/978-3-030-35802-0_24
Klíčová slova Graph drawing; Crossing number; Parameterized complexity; Vertex cover
Popis 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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