Abstract
A graph G is said to be faithfully embeddable on a closed surface \(F^2\) if G can be embedded on \(F^2\) in such a way that any automorphism of G extends to an auto-homeomorphism of \(F^2\). It has been known that every 3-connected planar graph is faithfully embeddable on the sphere. We shall show that every 3-connected planar graph is faithfully embeddable on a suitable orientable closed surface other than the sphere unless it is one of seven exceptions.
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Acknowledgments
The author would like to express his thanks to all participants of SIGMAP 2014 who gave him many good advices around his arguments on maps on surfaces. In particular, the notion of “Petrie duals” led him to a similar work on this topic with nonorientable closed surfaces. Also he appreciates Gašper Fijavž’s helpful discussion on Lemma 2 and an anonymous referee who taught him about Zelinka’s works.
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Negami, S. (2016). Faithful Embeddings of Planar Graphs on Orientable Closed Surfaces. In: Širáň, J., Jajcay, R. (eds) Symmetries in Graphs, Maps, and Polytopes. SIGMAP 2014. Springer Proceedings in Mathematics & Statistics, vol 159. Springer, Cham. https://doi.org/10.1007/978-3-319-30451-9_12
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DOI: https://doi.org/10.1007/978-3-319-30451-9_12
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