Drawing planar graphs of bounded degree with few slopes

We settle a problem of Dujmovic, Eppstein, Suderman, and Wood by showing that there exists a function f with the property that every planar graph G with maximum degree d admits a drawing with noncrossing straight-line edges, using at most f(d) different slopes. If we allow the edges to be represented by polygonal paths with one bend. then 2d slopes suffice. Allowing two bends per edge, every planar graph with maximum degree d >= 3 can be drawn using segments of at most [d/2] different slopes. There is only one exception: the graph formed by the edges of an octahedron is 4-regular, yet it requires 3 slopes. These bounds cannot be improved.

Published in:
Proc. 18th International Symposium on Graph Drawing
Presented at:
18th International Symposium on Graph Drawing
293-304, Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa

 Record created 2011-12-12, last modified 2018-03-17

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