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Nishina, Makoto; Suzuki, Yusuke
Discrete mathematics, October 2017, 2017-10-00, Letnik: 340, Številka: 10Journal Article
We shall determine exactly two (P,Q)-irreducible even triangulations of the projective plane. This result is a new generating theorem of even triangulations of the projective plane, that is, every even triangulation of the projective plane can be obtained from one of those two (P,Q)-irreducible even triangulations by a sequence of two expansions called a P-expansion and a Q-expansion, which were used in Batagelj (1984, 1989), Drapal and Lisonek (2010). Furthermore, we prove that for any closed surface F2 there are finitely many (P,Q)-irreducible even triangulations of F2.
