Generating polyhedral quadrangulations of the projective plane

Yusuke Suzuki

Abstract


We determine the 26 families of irreducible polyhedral quadrangulations of the projective plane under three reductions called a face-contraction, a 4-cycle removal and a 23-path shrink, which were first given by Batagelj in 1989. Every polyhedral quadrangulation of the projective plane can be obtained from one of them by a sequence of the inverse operations of the reductions.


Keywords


Quadrangulation, projective plane, generating theorem

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DOI: https://doi.org/10.26493/1855-3974.1195.c71

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