Diagonal flips in outer-Klein-bottle triangulations
The present paper deals with outer-Klein-bottle triangulations, i.e. two-cell embeddings of simple graphs \(G\) into the Klein bottle such that (i) each face is bounded by a cycle; (ii) there is a specific face \(F\), called outer face, on whose boundary cycle all vertices of \(G\) appear; and (iii) other faces are all triangular. In particular, the complete list of the 33 irreducible outer-Klein-bottle triangulations is determined (starting from the complete list of the 25 irreducible triangulations of the Klein bottle, obtained by \textit{S. Lawrencenko} and \textit{S. Negami} [J. Comb. Theory, Ser. B 70, No. 2, 265-291 (1997; Zbl 0876.05023)]). Moreover, any two outer-Klein-bottle triangulations with the same number of vertices are proved to be transformed into each other by a sequence of diagonal flips (see, for example, \textit{S. Negami} [Discrete Math. 135, No. 1-3, 225-232 (1994; Zbl 0823.05028)]).
scientific article; zbMATH DE number 1506816