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# An Efficient Algorithm for the Genus Problem with Explicit Construction of Forbidden Subgraphs

@inproceedings{Djidjev1991AnEA, title={An Efficient Algorithm for the Genus Problem with Explicit Construction of Forbidden Subgraphs}, author={Hristo Djidjev and John H. Reif}, booktitle={STOC}, year={1991} }

- Published 1991 in STOC
DOI:10.1145/103418.103456

We give an algorithm for irnbedding a graph G of n vertices onto an oriented surface of minimum genus g. If g z O then we also construct a forbidden subgraph of G which is homecjmorphic to a graph of size exp(O(g)! ) which cannot be irnbedded on a surface of genus g-1. Our algorithm takes sequential time exp(O(g)!)nO(l). Since exp(O (g)!) = exp(exp(O (glob))), our algorithm is polynomial time for genus g= O(loglog(n)/logloglog(,m)). A simple parallel implementation of our algorithm takes… CONTINUE READING

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