I was reading the book "Knot Theory and Its Applications" by Kunio Murasugi, he constructed the Seifert surface for a diagram of a knot, he also associated a graph to the Seifert surface where the disk of the Seifert surface are the vertices and two vertices are connected if there is a band in the Seifert surface that connect their disks. And the exercise 5.1.2 (a) says
Show that a Seifert graph is a plane graph. Further, show that it is also a bipartite plane graph.
I have already proved that the graph is bipartite but I don't know how to prove is plane. I read a equivalence of plane graphs about the graphs $K_{3,3}$ and $K_5$ but I think there is a more easy solution using the properties of the Seifert surface, any hint will help me a lot.