Layouts with wires of balanced length
Information and Computation
On the optimal layout of planar graphs with fixed boundary
SIAM Journal on Computing
An algorithm for drawing general undirected graphs
Information Processing Letters
A unified geometric approach to graph separators
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Optical Computing: Digital and Symbolic
Optical Computing: Digital and Symbolic
Algorithms for Drawing Graphs: An Annotated Bibliography
Algorithms for Drawing Graphs: An Annotated Bibliography
Area-efficient upward tree drawings
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Angles of planar triangular graphs
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Trees with convex faces and optimal angles
GD'06 Proceedings of the 14th international conference on Graph drawing
The straight-line RAC drawing problem is NP-hard
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Maximizing the total resolution of graphs
GD'10 Proceedings of the 18th international conference on Graph drawing
Optimal 3D angular resolution for low-degree graphs
GD'10 Proceedings of the 18th international conference on Graph drawing
Planar straight-line drawing in an O(n)×O(n) grid with angular resolution Ω(1/n)
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Triangulations with circular arcs
GD'11 Proceedings of the 19th international conference on Graph Drawing
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A famous theorem of I. Fa`ry states that any planar graph can be drawn in the plane so that all edges are straight-line segments and no two edges cross. The angular resolution of such a drawing is the minimum angle subtended by any pair of incident edges. The angular resolution of a planar graph is the maximum angular resolution over all such planar straight-line drawings of the graph. In a recent paper by Formann et al., Drawing graphs in the plane with high resolution, Symp. on Found. of Comp. Sci. (1990), 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 ≥ r(d)? We answer this question in the affirmative by showing that any planar graph of maximum degree d has angular resolution at least &agr;d radians where 0 G from &OHgr;(1/d), although currently, we are unable to settle this issue for general planar graphs. For the class of outerplanar graphs with triangulated interior and maximum degree d, although currently, we are unable to settle this issue for general planar graphs. For the class of outerplanar graphs with triangulated interior and maximum degree d, we show not only that &OHgr;(1/d) is lower bound on angular resolution, but in fact, this angular resolution can be achieved in a planar straight-line drawing where all interior faces are similar isosceles triangles. Additional results are contained in the full paper.