A graph G is an a-angle crossing (aAC) graph if every pair of crossing edges in G intersect at an angle of at least a. The concept of right angle crossing (RAC) graphs (a=Pi/2) was recently introduced by Didimo et. al. 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 aAC graphs for all 0 < a < Pi/2.
@article{arxiv.0908.3545,
title = {Notes on large angle crossing graphs},
author = {Vida Dujmovic and Joachim Gudmundsson and Pat Morin and Thomas Wolle},
journal= {arXiv preprint arXiv:0908.3545},
year = {2013}
}