Crossing numbers and skewness of some generalized petersen graphs

Abstract

The skewness of a graph G is the minimum number of edges in G whose removal results in a planar graph. In this paper, we show that the skewness of the generalized Petersen graph P(3k, k) is [k/2] + 1, where k ≥ 4. As a byproduct, it is shown that for k ≥ 4, [k/2} + 1 ≤ cr(P(3k,k)) ≤ k, where cr(G) denotes the crossing number of G. © Springer-Verlag Berlin Heidelberg 2005.