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Crossing angles of geometric graphs

By Karin Arikushi and Csaba D. Tóth

Abstract

We study the crossing angles of geometric graphs in the plane. We introduce the crossing angle number of a graph G, denoted can(G), which is the minimum number of angles between crossing edges in a straight-line drawing of G. We show that an n-vertex graph G with can(G) = O(1) has O(n) edges, but there are graphs G with bounded degree and arbitrarily large can(G). We also initiate the study of global crossing angle rigidity for geometric graphs. We construct bounded degree graphs G = (V,E) such that for any two straight-line drawings of G with the same crossing angle pattern, there is a subset V ′ ⊂ V of |V ′ | ≥ |V |/2 vertices that are embedded into similar point sets in the two drawings

Topics: Communicated by
Year: 2014
DOI identifier: 10.7155/jgaa.00329
OAI identifier: oai:CiteSeerX.psu:10.1.1.453.170
Provided by: CiteSeerX
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