Uniqueness and minimality of large face-width embeddings of graphs

Abstract

LetG be a graph embedded in a surface of genusg. It is shown that if the face-width of the embedding is at leastclog(g)/loglog(g), then such an embedding is unique up to Whitney equivalence. If the face-width is at leastclog(g), then every embedding ofG which is not Whitney equivalent to our embedding has strictly smaller Euler characteristic.

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Supported in part by the Ministry of Science and Technology of Slovenia, Research Project P1-0210-101-94.

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Mohar, B. Uniqueness and minimality of large face-width embeddings of graphs. Combinatorica 15, 541–556 (1995). https://doi.org/10.1007/BF01192526

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Mathematical Subject Classification (1991)

  • 05 C 10