page_title: Planar cover
hierarchical_section_title: Planar cover
context_page_description: In graph theory, a planar cover of a finite graph G is a finite covering graph of G that is itself a planar graph. Every graph that can be embedded into the projective plane has a planar cover; an unsolved conjecture of Seiya Negami states that these are the only graphs with planar covers.
  The existence of a planar cover is a minor-closed graph property, and so can be characterized by finitely many forbidden minors, but the exact set of forbidden minors is not known. For the same reason, there exists a polynomial time algorithm for testing whether a given graph has a planar cover, but an explicit description of this algorithm is not known.
context_section_description: In graph theory, a planar cover of a finite graph G is a finite covering graph of G that is itself a planar graph. Every graph that can be embedded into the projective plane has a planar cover; an unsolved conjecture of  Seiya Negami states that these are the only graphs with planar covers.
  The existence of a planar cover is a minor-closed graph property, and so can be characterized by finitely many forbidden minors, but the exact set of forbidden minors is not known. For the same reason, there exists a polynomial time algorithm for testing whether a given graph has a planar cover, but an explicit description of this algorithm is not known.
caption: The graph C is a planar cover of the graph H. The covering map is indicated by the vertex colors.