Abstract
Whitney's theorem states that 3-connected planar graphs admit essentially unique embeddings in the plane. We generalize this result to embeddings of graphs in arbitrary surfaces by showing that there is a function ξ:N0→N0 such that every 3-connected graph admits at most ξ(g) combinatorially distinct embeddings of face-width ⩾3 into surfaces whose Euler genus is at most g.
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