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Planar cover
Graph theory concept / From Wikipedia, the free encyclopedia
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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.[1]
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The existence of a planar cover is a minor-closed graph property,[2] 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.