On the Angular Resolution of Planar Graphs

  • Authors:
  • Seth Malitz;Achilleas Papakostas

  • Affiliations:
  • -;-

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 1994

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Abstract

It is a well-known fact that every planar graph admits a planar straight-line drawing. The angular resolution of such a drawing is the minimum angle subtended by any pair of incident edges. The angular resolution of the graph is the supremum angular resolution over all planar straight-line drawings of the graph. In a recent paper by Formann et al. [Proc. 31st IEEE Sympos. on Found. of Comput. Sci., 1990, pp. 86-95], the following question is posed: Does there exist a constant $r(d) 0$ such that every planar graph of maximum degree $d$ has angular resolution $\geq r(d)$ radians? The present authors show that the answer is yes and that it follows easily from results in the literature on disk-packings. The conclusion is that every planar graph of maximum degree $d$ has angular resolution at least $\alpha^d$ radians, $0