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)
|
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)
|
of the complete bipartite graph by
(3)
|
and of the hypercube graph by
(4)
|
(Cimikowski 1992).