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The closed 2-cell embeddings of 2-connected doubly toroidal graphs

✍ Scribed by Xiaoya Zha

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
711 KB
Volume
145
Category
Article
ISSN
0012-365X

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✦ Synopsis

A closed 2-cell embedding of a graph embedded in some surface is an embedding such that each face is bounded by a circuit in the graph. The closed 2-cell embedding conjecture says that every 2-connected graph has a closed 2-cell embedding in some surface. In this paper, we prove that any 2-connected doubly toroidal graph G has a closed 2-cell embedding in some surface. As a corollary, such a graph has a cycle double cover; i.e., G has a set of circuits containing every edge exactly twice.

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