Topological Book Embedding of Bipartite Graphs

A topological book embedding of a graph is an embedding in a book that carries the vertices in the spine of the book and the edges in the pages so that edges are allowed to cross the spine. Recently, the author has shown that for an arbitrary graph G with n vertices there exists a d + 1page book embedding of G in which each edge crosses the spine logd n times. This paper improves the result for the case of bipartite graphs and shows that there exists a d + 1-page book embedding of a bipartite graph Gn1 ,n2 having two partite sets with n1 and n2 vertices respectively (n1 ≥ n2) in which each edge crosses the spine logd n2 − 1 times. key words: bipartite graph, book embedding, crossings of edges over the spine, page-number