A Proof Technique for Skewness of Graphs

The skewness of a graph G is the minimum number of edges in G whose removal results in a planar graph. By appropriately introducing a weight to each edge of a graph, we determine, among other thing, the skewness of the generalized Petersen graph P(4k, k) for odd k at least 9. This provides an answer to the conjecture raised in [3].