Flexibility of Embeddings of Bouquets of Circles on the Projective Plane and Klein Bottle

Abstract

In this paper, we study the flexibility of embeddings of bouquets of circles on the projective plane and the Klein bottle. The numbers (of equivalence classes) of embeddings of bouquets of circles on these two nonorientable surfaces are obtained in explicit expressions. As their applications, the numbers (of isomorphism classes) of rooted one-vertex maps on these two nonorientable surfaces are deduced.