The Complexity of the Graph Embedding Problem
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(v3) 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(v10) algorithm for constructing an embedding or answering that no embedding exists.
Keywordsgenus embedding computational complexity NP-complete
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