Graph drawings with few slopes
نویسندگان
چکیده
منابع مشابه
Graph drawings with few slopes
The slope-number of a graph G is the minimum number of distinct edge slopes in a straight-line drawing of G in the plane. We prove that for ∆ ≥ 5 and all large n, there is a ∆-regular n-vertex graph with slope-number at least n1− 8+ε ∆+4 . This is the best known lower bound on the slope-number of a graph with bounded degree. We prove upper and lower bounds on the slope-number of complete bipart...
متن کاملOuterplanar Graph Drawings with Few Slopes
We consider straight-line outerplanar drawings of outerplanar graphs in which a small number of distinct edge slopes are used, that is, the segments representing edges are parallel to a small number of directions. We prove that ∆ − 1 edge slopes suffice for every outerplanar graph with maximum degree ∆ > 4. This improves on the previous bound of O(∆), which was shown for planar partial 3-trees,...
متن کاملGraph Drawings with One Bend and Few Slopes
We consider drawings of graphs in the plane in which edges are represented by polygonal paths with at most one bend and the number of different slopes used by all segments of these paths is small. We prove that d 2 e edge slopes suffice for outerplanar drawings of outerplanar graphs with maximum degree ∆ > 3. This matches the obvious lower bound. We also show that d 2 e + 1 edge slopes suffice ...
متن کاملGraph Drawings with Few Slopes * Dedicated to Godfried Toussaint on His 60th Birthday
The slope-number of a graph G is the minimum number of distinct edge slopes in a straight-line drawing of G in the plane. We prove that for ∆ ≥ 5 and all large n, there is a ∆-regular n-vertex graph with slope-number at least n 8+ε ∆+4 . This is the best known lower bound on the slope-number of a graph with bounded degree. We prove upper and lower bounds on the slope-number of complete bipartit...
متن کاملDrawings of planar graphs with few slopes and segments
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 52n segments and at most 2n slopes. We prove that every cubic 3-connected plane graph has a plane dr...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2007
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2006.08.002