Strong Embeddings of Outer Planar Near-triangulations on Non-orientable Surfaces

Let N t be an outer planar near triangulation of order n . In this paper, we present an interpolation theorem for strong embeddings N t on non orientable surfaces, i.e., for any q, 1≤q≤n(Δ) , there exists a strong embedding μ(N t) of N t on the non orientable surface Q q , where n(Δ) is the number of interior triangles of N t and q be the genus of the surface Q q . Moreover, the set of face boundaries of μ(N t) is an SCDC (small circuits double cover) C of N t , |C|= n-q-1 , and the dual of N t with respect to C is also a planar graph. Being a corollary, for an outer planar graph G , letting n(Δ) be the number of interior triangles of G , we obtain a similar result.