The skewness of a graph is the minimum number of edges whose removal results in a planar graph (Harary 1994, p. 124). The skewness is sometimes denoted (Cimikowski 1992).
A graph with has toroidal crossing number . (However, there exist graphs with that still have .)
satisfies
(1)
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where is the vertex count of and its edge count (Cimikowski 1992).
The skewness of a disconnected graph is equal to the sum of skewnesses of its connected components.
The skewness of a complete graph is given by
(2)
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of the complete bipartite graph by
(3)
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and of the hypercube graph by
(4)
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(Cimikowski 1992).