Diagonal Transformations and Cycle Parities of Quadrangulations on Surfaces

@article{Nakamoto1996DiagonalTA,
  title={Diagonal Transformations and Cycle Parities of Quadrangulations on Surfaces},
  author={Atsuhiro Nakamoto},
  journal={J. Comb. Theory, Ser. B},
  year={1996},
  volume={67},
  pages={202-211}
}
A quadrangulation G on a closed surface F 2 is a simple graph embedded in F 2 so that each face of G is quadrilateral. The diagonal slide and the diagonal rotation were defined in [1] as two transformations of quadrangulations. See Fig. 1. We also call the both transformations diagonal transformations in total. If the graph obtained by a diagonal slide is not a simple graph, then we do not apply it. If two quadrangulations G1 and G2 on a closed surface F 2 can be transformed into each other by… CONTINUE READING