Crossing Angles of Geometric Graphs
نویسندگان
چکیده
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. Submitted: Februray 2014 Reviewed: April 2014 Revised: May 2014 Accepted: June 2014 Final: July 2014 Published: July 2014 Article type: Regular paper Communicated by: G. Liotta A preliminary version of this paper has been presented at the 6th Annual Conference on Combinatorial Optimization and Applications (Banff, AB, 2012) [3]. Research supported in part by the NSERC grant RGPIN 35586. E-mail addresses: [email protected] (Karin Arikushi) [email protected] (Csaba D. Tóth) 402 Arikushi and Tóth Crossing Angles of Geometric Graphs
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