The Complexity of the Graph Embedding Problem

  • D. Archdeacon


We investigate the computational complexity of determining if a graph G on v vertices embeds in a surface S. Robertson and Seymour have given an O(v 3) decision algorithm for this embedding problem. We show here how the use the yes/no output from their algorithm to construct the embedding, that is, we self-reduce the search algorithm to the decision algorithm. We conclude that for each fixed surface S there exists an O(v 10) algorithm for constructing an embedding or answering that no embedding exists.


genus embedding computational complexity NP-complete 


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Copyright information

© Physica-Verlag Heidelberg 1990

Authors and Affiliations

  • D. Archdeacon
    • 1
  1. 1.BurlingtonUSA

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