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Crossing angles of geometric graphs

By Karin Arikushi and Csaba D. Tóth


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:
Provided by: CiteSeerX
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