The skewness of a graph G is the minimum number of edges whose removal results in a planar graph. The skewness is sometimes denoted μ(G). A graph G with μ(G)<2 has toroidal crossing number cr_1(G) = 0. (However, there exist graphs with μ(G)>=2 that still have cr_1(G) = 0.) μ(G) satisfies μ(G)>=m - (3n - 6), where n>2 is the vertex count of G and m its edge count. The skewness of a disconnected graph is equal to the sum of skewnesses of its connected components.

apex graph | critical nonplanar graph | graph coarseness | planar graph | toroidal crossing number | toroidal graph