Embedding K5 and K3,3 on orientable surfaces

Gagarin, Andrei ORCID: https://orcid.org/0000-0001-9749-9706 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:	07 Nov 2022 10:33
URI:	https://orca.cardiff.ac.uk/id/eprint/132615

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