On the skewness of Cartesian products with trees

Abstract

The skewness of a graph G is the minimum number of edges in G whose removal results in a planar graph. It is a parameter that measures how non-planar a graph is, and it also has important applications to VLSI design, but there are few results for skewness of graphs. In this paper, we first prove that the skewness is additive for the Zip product under certain conditions. We then present results on the lower bounds for the skewness of Cartesian products of graphs with trees and paths, respectively. Some exact values of the skewness for Cartesian products of complete graphs with trees, as well as of stars and wheels with paths are obtained by applying these lower bounds.