Minimal embeddings in the projective plane

  title={Minimal embeddings in the projective plane},
  author={Scott P. Randby},
  journal={Journal of Graph Theory},
We show that if G is a graph embedded on the projective plane in such a way that each noncontractible cycle intersects G at least n times and the embedding is minimal with respect to this property (i.e., the representativity of the embedding is n), then G can be reduced by a series of reduction operations to an n × n × n projective grid. The reduction operations consist of changing a triangle of G to a triad, changing a triad of G to a triangle, and several others. We also show that if every… CONTINUE READING