Title

On The Flexibility Of Toroidal Embeddings

Keywords

Embedding; Flexibility; Representativity; Torus

Abstract

Two embeddings Ψ1 and Ψ2 of a graph G in a surface Σ are equivalent if there is a homeomorphism of Σ to itself carrying Ψ1 to Ψ2. In this paper, we classify the flexibility of embeddings in the torus with representativity at least 4. We show that if a 3-connected graph G has an embedding Ψ in the torus with representativity at least 4, then one of the following holds: (i)Ψ is the unique embedding of G in the torus;(ii)G has three nonequivalent embeddings in the torus, G is the 4-cube Q4 (or C4 × C4), and each embedding of G forms a 4-by-4 toroidal grid;(iii)G has two nonequivalent embeddings in the torus, and G can be obtained from a toroidal 4-by-4 grid (faces are 2-colored) by splitting i(i ≤ 16) vertices along one-colored faces and replacing j(j ≤ 16) other colored faces with planar patches. © 2007 Elsevier Inc. All rights reserved.

Publication Date

1-1-2008

Publication Title

Journal of Combinatorial Theory. Series B

Volume

98

Issue

1

Number of Pages

-

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jctb.2007.03.006

Socpus ID

36048991248 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/36048991248

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