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 کاملCrooked Diagrams with Few Slopes
A natural and practical criterion in the preparation of diagrams of ordered sets is to minimize the number of different slopes used for the edges. Any diagram requires at least the maximum number of upper covers (or of lower covers) of any element. While this maximum degree is not always enough we show that it is as long as any edge joining a covering pair may be bent, to produce a crooked diag...
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 کاملDrawing Planar Graphs of Bounded Degree with Few Slopes
We settle a problem of Dujmović, 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 pl...
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 ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1986
ISSN: 0012-365X
DOI: 10.1016/0012-365x(86)90012-9