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Minimal Quadrangulations of Surfaces by Wenzhong Liu; M.N. Ellingham; Dong Ye is a Computer Science article available to read on EtoBox.

What is Minimal Quadrangulations of Surfaces about?

A quadrangular embedding of a graph in a surface Σ, also known as a quadrangulation of Σ, is a cellular embedding in which every face is bounded by a 4-cycle. A quadrangulation of Σ is minimal if there is no quadrangular embedding of a (simple) graph of smaller order in Σ. In this paper we determine n(Σ), the order of a minimal quadrangulation of a surface Σ, for all surfaces, both orientable and nonorientable. Letting S 0 denote the sphere and N 2 the Klein bottle, we prove that n(S 0 ) = 4, n(N 2 ) = 6, and n(Σ) = (5 + 25 -16χ(Σ))/2 for all other surfaces Σ, where χ(Σ) is the Euler characteristic. Our proofs use a 'diagonal technique', introduced by Hartsfield in 1994. We explain the general features of this method.

Who reads Minimal Quadrangulations of Surfaces?

Author

Wenzhong Liu; M.N. Ellingham; Dong Ye

Publisher

Elsevier BV

Published

2022

Language

EN

Field

Computer Science (Physical Sciences)