Embedding a graph in the grid of a surface with the minimum number of bends is NP-hard

  • M. A. Garrido
  • A. Márquez
Left and Right Turns
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)


This paper is devoted to the study of graph embeddings in the grid of non-planar surfaces. We provide an adequate model for those embeddings and we study the complexity of minimizing the number of bends. In particular, we prove that testing whether a graph admits a rectilinear (without bends) embedding essentially equivalent to a given embedding, and that given a graph, testing if there exists a surface such that the graph admits a rectilinear embedding in that surface are NP-complete problems and hence the corresponding optimization problems are NP-hard.


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • M. A. Garrido
    • 1
  • A. Márquez
    • 1
  1. 1.Dept. Matemática Aplicada IUniversidad de SevillaSevillaSpain

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