Combinatorial Structure of Faces in Triangulations on Surfaces

The degree of a vertex or face in a graph on the plane or other orientable surface is the number of incident edges. A face is of type if whenever . We denote the minimum vertex-degree of  by  . The purpose of our paper is to prove that every triangulation with of the torus, as well as of large enoug...

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Bibliographic Details
Published in:Siberian mathematical journal 2022-07, Vol.63 (4), p.662-669
Main Authors: Borodin, O. V., Ivanova, A. O.
Format: Article
Language:English
Subjects:
Combinatorial analysis
Mathematics
Mathematics and Statistics
Toruses
Triangulation
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Summary:The degree of a vertex or face in a graph on the plane or other orientable surface is the number of incident edges. A face is of type if whenever . We denote the minimum vertex-degree of  by  . The purpose of our paper is to prove that every triangulation with of the torus, as well as of large enough such a triangulation of any fixed orientable surface of higher genus has a face of one of the types , , , , , or , where all parameters are best possible.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446622040061