425 KB24 KB200820252016Suzuki, Yusukeletnik:10številka:2str. 281-290COBISSID:17833049ISSN:1855-3966URN:URN:NBN:SI:doc-IO1HCTW9enUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneaclosed surfacegenerating theoremizrek o generiranjukvadrangulacijaquadrangulationsklenjena ploskevCube-contractions in 3-connected quadrangulations|A 3-connected quadrangulation of a closed surface is said to be ?$\mathcal{K}_3^\prime$?-irreducible if no face-or cube-contraction preserves simplicity and 3-connectedness. In this paper, we prove that a ?$\mathcal{K}_3^\prime$?-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 ?$F_0\subseteq F(H)$? where ?$F(H)$? stands for the set of faces of ?$H$?. We also determine ?$\mathcal{K}_3^\prime$?-irreducible quadrangulations of the sphere and the projective plane. These results imply new generating theorems of 3-connected quadrangulations of closed surfacesZa 3-povezano kvadrangulacijo sklenjene ploskve pravimo, da je ?$\mathcal{K}_3^\prime$?-ireducibilna, če nobena skrčtev lic oziroma kock ne ohranja enostavnosti in 3-povezanosti. V tem članku dokažemo, da je ?$\mathcal{K}_3^\prime$?-ireducibilna kvadrangulacija sklenjene ploskve z izjemo sfere in projektivne ravnine bodisi (i) ireducibilna bodisi (ii) jo lahko dobimo iz ireducibilne kvadrangulacije ?$H$? z dodajanjem 4-ciklov k ?$F_0\subseteq F(H)$?, kjer $F(H)$ pomeni množico lic kvadrangulacije ?$H$?. Določimo tudi ?$\mathcal{K}_3^\prime$?-ireducibilne kvadrangulacije sfere in projektivne ravnine. Ti rezultati implicirajo nove izreke o generiranju 3-povezanih kvadrangulacij sklenjenih ploskevTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije