A new upper bound for angular resolution

09/15/2023

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by   Hiroyuki Miyata, et al.

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The angular resolution of a planar straight-line drawing of a graph is the smallest angle formed by two edges incident to the same vertex. Garg and Tamassia (ESA '94) constructed a family of planar graphs with maximum degree d that have angular resolution O((log d)^1/2/d^3/2) in any planar straight-line drawing. This upper bound has been the best known upper bound on angular resolution for a long time. In this paper, we improve this upper bound. For an arbitrarily small positive constant ε, we construct a family of planar graphs with maximum degree d that have angular resolution O((log d)^ε/d^3/2) in any planar straight-line drawing.