Finitizable set of reductions for polyhedral quadrangulations of closed surfaces

Yusuke Suzuki

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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DOI: 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