Small Drawings of Outerplanar Graphs,Series-Parallel Graphs,and Other Planar Graphs |
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Authors: | Therese Biedl |
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Institution: | 1.David R. Cheriton School of Computer Science,University of Waterloo,Waterloo,Canada |
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Abstract: | In this paper, we study small planar drawings of planar graphs. For arbitrary planar graphs, Θ(n
2) is the established upper and lower bound on the worst-case area. A long-standing open problem is to determine for what graphs
a smaller area can be achieved. We show here that series-parallel graphs can be drawn in O(n
3/2) area, and outerplanar graphs can be drawn in O(nlog n) area, but 2-outerplanar graphs and planar graphs of proper pathwidth 3 require Ω(n
2) area. Our drawings are visibility representations, which can be converted to polyline drawings of asymptotically the same
area. |
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Keywords: | |
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