, Volume 49, Issue 1, pp 1–11 | Cite as

Algorithms for Graphs Embeddable with Few Crossings per Edge

  • Alexander GrigorievEmail author
  • Hans L. BodlaenderEmail author


We consider graphs that can be embedded on a surface of bounded genus such that each edge has a bounded number of crossings. We prove that many optimization problems, including maximum independent set, minimum vertex cover, minimum dominating set and many others, admit polynomial time approximation schemes when restricted to such graphs. This extends previous results by Baker and Eppstein to a much broader class of graphs. We also prove that for the considered class of graphs, there are balanced separators of size \(O(\sqrt{n})\) where n is a number of vertices in the graph. On the negative side, we prove that it is intractable to recognize the graphs embeddable in the plane with at most one crossing per edge.


Planar Graph Tree Decomposition Polynomial Time Approximation Scheme Unit Disk Graph Planar Embedding 
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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Faculty of Economics and Business Administration, Department of Quantitative Economics, Maastricht University, P.O. Box 6166200 MD MaastrichtThe Netherlands
  2. 2.Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, De Uithof, P.O. Box 800893508 TB UtrechtThe Netherlands

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