Book embedding of locally planar graphs on orientable surfaces

A book embedding   of a graph GG is an embedding of vertices of GG along the spine   of a book, and edges of GG on the pages   so that no two edges on the same page intersect. Malitz (1994) proved that any graph on the orientable surface SgSg of genus gg has a book embedding with O(g) pages. In this paper, we prove that every locally planar   graph on SgSg (i.e., one with high representativity) has a book embedding with seven pages.