A book embedding of a graph G consists of placing the vertices of G on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is a measure of the quality of a book embedding which is the minimum number of pages in which the graph G can be embedded.
Let $G$ is a finite covering graph of a graph $B$. The covering graph is more complicated than the basis graph. Hence at the beginning , I thought that $pn(G)$ should be no less than $pn(B)$ in general. Until Jan Kyncl give a counter-example: The graph of the icosahedron is a 2-fold cover of K6, but $pn(icosahedron)=2$ , $pn(K_6)=3$. Does $pn(G)\geq pn(B)-1 $ hold in general?