Notes on large angle crossing graphs

Notes on large angle crossing graphs

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...

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Veröffentlicht in:arXiv.org 2010-11
Hauptverfasser: Dujmovic, Vida, Gudmundsson, Joachim, Morin, Pat, Wolle, Thomas
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Computer Science - Computational Geometry
Computer Science - Data Structures and Algorithms
Graph theory
Graphs
Lower bounds
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Zusammenfassung: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0908.3545