منابع مشابه
A simple proof for open cups and caps
Let X be a set of points in general position in the plane. General position means that no three points lie on a line and no two points have the same x-coordinate. Y ⊆ X is a cup, resp. cap, if the points of Y lie on the graph of a convex, resp. concave function. Denote the points of Y by p1, p2, . . . , pm according to the increasing x-coordinate. The set Y is open in X if there is no point of ...
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Given a set S of n points in the plane, we compute in time O(n) the total number of convex polygons whose vertices are a subset of S. We give an O(m n) algorithm for computing the number of convex k-gons with vertices in S, for all values k = 3; : : : ;m; previously known bounds were exponential (O(ndk=2e)). We also compute the number of empty convex polygons (resp., k-gons, k m) with vertices ...
متن کاملEmpty Convex Hexagons in Planar Point Sets
Erdős asked whether every sufficiently large set of points in general position in the plane contains six points that form a convex hexagon without any points from the set in its interior. Such a configuration is called an empty convex hexagon. In this paper, we answer the question in the affirmative. We show that every set that contains the vertex set of a convex 9-gon also contains an empty co...
متن کاملEmpty convex polygons in planar point sets
The Erdős–Szekeres theorem inspired a lot of research. A frequent topic in this area is the study of the existence of so-called empty convex polygons in finite planar point sets. Let P be a finite set of points in general position in the plane. A convex k-gon G is called a k-hole (or empty convex k-gon) of P , if all vertices of G lie in P and no point of P lies inside G. Frequently we will mea...
متن کاملPartitions of planar point sets into polygons
In this paper, we characterize planar point sets that can be partitioned into disjoint polygons of arbitrarily specified sizes. We provide an algorithm to construct such a partition, if it exists, in polynomial time. We show that this problem is equivalent to finding a specified 2-factor in the visibility graph of the point set. The characterization for the case where all cycles have length 3 a...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2007
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-006-1286-3