On the skewness of graphs / Sim Kai An - Sim, Kai An (2014)
Let G be a graph. The crossing number of G, denoted as cr(G), is the minimum number of crossings of its edges among all drawings of G in the plane. The skewness of a graph G, denoted as sk(G), is the minimum number of edges in G whose deletion results in a planar graph. In Chapter 1 of this thesis, some preliminaries and denitions concerning graphs are given. In Chapter 2, we present some known results on crossing numbers of graphs and also a planarity criterion for a graph. In Chapter 3, we provide a survey on skewness of graphs and introduce some graphs which are The main results of this thesis are presented in the last chapter. We prove some results concerning the skewness for the join of two graphs. We then use these results to determine completely the skewness of complete k-partite graphs for k = 2, 3, 4.