# An FPT algorithm for the embeddability of graphs into two-dimensional simplicial complexes

@inproceedings{Verdire2021AnFA, title={An FPT algorithm for the embeddability of graphs into two-dimensional simplicial complexes}, author={{\'E}ric Colin de Verdi{\`e}re and Thomas Magnard}, booktitle={ESA}, year={2021} }

We consider the embeddability problem of a graph G into a two-dimensional simplicial complex C: Given G and C, decide whether G admits a topological embedding into C. The problem is NP-hard, even in the restricted case where C is homeomorphic to a surface. It is known that the problem admits an algorithm with running time f(c)n, where n is the size of the graph G and c is the size of the two-dimensional complex C. In other words, that algorithm is polynomial when C is fixed, but the degree of… Expand

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