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Embedding K5 and K3,3 on orientable surfaces

Gagarin, Andrei and Kocay, William 2020. Embedding K5 and K3,3 on orientable surfaces. Presented at: 18th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, Ischia, Italy (online), 14-16 September 2020.

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Abstract

The Kuratowski graphs K5 and K3,3 are fundamental non-planar graphs. We are interested in obtaining all their distinct 2-cell embeddings on orientable surfaces. The 2-cell embeddings of K5 and K3,3 on the torus are well-known. Using a constructive approach of expanding from minors, we obtain all 2-cell embeddings of these graphs on the double torus. As a consequence, several new polygonal representations of the double torus are described. Rotation systems for the one-face embeddings of K5 on the triple torus are also found, using an exhaustive search approach.

Item Type: Conference or Workshop Item (Paper)
Status: In Press
Schools: Mathematics
Date of First Compliant Deposit: 18 June 2020
Date of Acceptance: 9 June 2020
Last Modified: 16 Sep 2020 02:05
URI: http://orca.cf.ac.uk/id/eprint/132615

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