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
Copyright Status
Unknown
Socpus ID
36048991248 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/36048991248
STARS Citation
Robertson, Neil; Zha, Xiaoya; and Zhao, Yue, "On The Flexibility Of Toroidal Embeddings" (2008). Scopus Export 2000s. 11011.
https://stars.library.ucf.edu/scopus2000/11011