Minimal quadrangulations of surfaces
نویسندگان
چکیده
A quadrangular embedding of a graph in surface Σ, also known as quadrangulation is cellular which every face bounded by 4-cycle. Σ minimal if there no (simple) smaller order Σ. In this paper we determine n(Σ), the for all surfaces, both orientable and nonorientable. Letting S0 denote sphere N2 Klein bottle, prove that n(S0)=4,n(N2)=6, n(Σ)=⌈(5+25−16χ(Σ))/2⌉ other surfaces where χ(Σ) Euler characteristic. Our proofs use ‘diagonal technique’, introduced Hartsfield 1994. We explain general features method.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2022
ISSN: ['0095-8956', '1096-0902']
DOI: https://doi.org/10.1016/j.jctb.2022.06.003