**Drawings of planar graphs with few slopes and segments.**

V. Dujmović, D. Eppstein, M. Suderman, and D. R. Wood.

arXiv:math.CO/0606450.

*Comp. Geom. Theory & Applications*38: 194–212, 2007.We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes. We prove that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface).

Co-authors – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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