Drawing orders with few slopes
نویسندگان
چکیده
منابع مشابه
Drawing 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 کاملDrawing Outer 1-planar Graphs with Few Slopes
A graph is outer 1-planar if it admits a drawing where each vertex is on the outer face and each edge is crossed by at most another edge. Outer 1-planar graphs are a superclass of the outerplanar graphs and a subclass of the planar partial 3-trees. We show that an outer 1-planar graph G of bounded degree ∆ admits an outer 1-planar straight-line drawing that uses O(∆) different slopes, which gen...
متن کاملGraph 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 کاملDrawing Permutations with Few Corners
A permutation may be represented by a collection of paths in the plane. We consider a natural class of such representations, which we call tangles, in which the paths consist of straight segments at 45 degree angles, and the permutation is decomposed into nearest-neighbour transpositions. We address the problem of minimizing the number of crossings together with the number of corners of the pat...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90201-r