Exact Crossing Number Parameterized by Vertex Cover

  • Petr HliněnýEmail author
  • Abhisekh Sankaran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11904)


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.


Graph drawing Crossing number Parameterized complexity Vertex cover 


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Authors and Affiliations

  1. 1.Faculty of Informatics of Masaryk UniversityBrnoCzech Republic
  2. 2.Department of Computer Science and TechnologyUniversity of CambridgeCambridgeUK

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