The Slope Number of $K_{n,m}$

Viola Meszaros

University of Szeged

Abstract

Let G be a finite graph with no loops or multiple edges. By a drawing of G we mean a representation of G in the plane such that each vertex is represented by a distinct point and each edge by a straight-line segment connecting the corresponding two points. No edge passes through any other vertex than its endpoints. Every edge determines a slope.

The slope number of G-denoted by sl(G)- is the smallest integer s such that s slopes are sufficient to draw the graph G. It is easy to see that sl(K_n)=n. The case of K_{n,m} is more complicated. The goal of the talk is to analyze it and give some lower and upper bounds for it.