منابع مشابه
Crooked 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 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 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 کاملVenn Diagrams with Few Vertices
An n-Venn diagram is a collection of n finitely-intersecting simple closed curves in the plane, such that each of the 2n sets X1∩X2∩· · ·∩Xn, where each Xi is the open interior or exterior of the i-th curve, is a non-empty connected region. The weight of a region is the number of curves that contain it. A region of weight k is a k-region. A monotone Venn diagram with n curves has the property t...
متن کاملLattice 3-Polytopes with Few Lattice Points
This paper is intended as a first step in a program for a full algorithmic enumeration of lattice 3-polytopes. The program is based in the following two facts, that we prove: • For each n there is only a finite number of (equivalence classes of) 3polytopes of lattice width larger than one, where n is the number of lattice points. Polytopes of width one are infinitely many, but easy to classify....
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1991
ISSN: 0097-3165
DOI: 10.1016/0097-3165(91)90025-c