Finitizable set of reductions for polyhedral quadrangulations of closed surfaces
Abstract
In this paper, we discuss generating theorems of polyhedral quadrangulations of closed surfaces. We prove that the set of the eight reductional operations {R1, …, R8} defined for polyhedral quadrangulations is finitizable for any closed surface F2, that is, there exist finitely many minimal polyhedral quadrangulations of F2 using such operations R1, …, R7 and R8. Furthermore, we show that any proper subset of {R1, …, R8} is not finitizable for polyhedral quadrangulations of the torus.
Keywords
Generating theorem, reduction, finitizable set, polyhedral quadrangulation
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MANUSCRIPTDOI: https://doi.org/10.26493/1855-3974.2704.31a
ISSN: 1855-3974
Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications