Geodesic
Cube-contractions in 3-connected quadrangulations
Ars Mathematica Contemporanea, Tome 10 (2016) no. 2, pp. 281-290.

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A 3-connected quadrangulation of a closed surface is said to be Kʹ3-irreducible if no face- or cube-contraction preserves simplicity and 3-connectedness. In this paper, we prove that a Kʹ3-irreducible quadrangulation of a closed surface except the sphere and the projective plane is either (i) irreducible or (ii) obtained from an irreducible quadrangulation H by applying 4-cycle additions to F0 ⊆ F(H) where F(H) stands for the set of faces of H. We also determine Kʹ3-irreducible quadrangulations of the sphere and the projective plane. These results imply new generating theorems of 3-connected quadrangulations of closed surfaces.
DOI : 10.26493/1855-3974.552.bf3
Keywords: Quadrangulation, closed surface, generating theorem 
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Yusuke Suzuki. Cube-contractions in 3-connected quadrangulations. Ars Mathematica Contemporanea, Tome 10 (2016) no. 2, pp. 281-290. doi : 10.26493/1855-3974.552.bf3. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.552.bf3/

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