It is proved that the decision problem about the existence of an embedding of face-width 3 of a given graph is NP-complete. A similar result is proved for some related decision problems. This solves a problem raised by Neil Robertson.
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Received July 6, 1998
ID="*" Supported in part by the Ministry of Science and Technology of Slovenia, Research Project J1–0502–0101–98.
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Mohar, B. Existence of Polyhedral Embeddings of Graphs. Combinatorica 21, 395–401 (2001). https://doi.org/10.1007/s004930100003
- AMS Subject Classification (2000) Classes: 05C10, 68Q17