#

### CJTCS Special Issue: CATS 2010

### Selected papers from

# 2010 Computing: The Australasian Theory Symposium

### held in Brisbane, Australia, January 18-21 2010.

## Guest Editors: Taso Viglas, University of Sydney, Australia

## Alex Potanin, Victoria University, Wellington, NZ

#### Article 2011-4

Published by the Department of Computer Science, The University of Chicago.

####
Notes on Large Angle Crossing Graphs

Vida Dujmovic

Computational Geometry Lab

School of Computer Science

Carleton University

`vida [at] cs [dot] mcgill [dot] ca`,

Joachim Gudmundsson

NICTA

Sydney

Australia

joachim.gudmundsson [at] gmail [dot] com,

Pat Morin

Computational Geometry Lab

School of Computer Science

Carleton University

`morin [at] scs [dot] carleton [dot] ca`,

and

Thomas Wolle

NICTA

Sydney

Australia

`thomas.wolle [at] gmail [dot] com`

*May 6, 2011*
##### Abstract

A geometric graph G is an a angle crossing (alpha AC) graph if every pair of
crossing edges in G cross at an angle of at least alpha. The concept of right angle crossing
(RAC) graphs alpha = pi/2) was recently introduced by Didimo et al. [10]. It was shown that
any RAC graph with n vertices has at most 4n-10 edges and that there are infinitely many
values of n for which there exists a RAC graph with n vertices and 4n-10 edges. In this
paper, we give upper and lower bounds for the number of edges in alphaAC graphs for all
0 < alpha < pi/2.

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2011, Article 5
2011 Article 3

Special Issue
Published articles