Coloring half-planes and bottomless rectangles
نویسندگان
چکیده
منابع مشابه
Coloring half-planes and bottomless rectangles
We prove lower and upper bounds for the chromatic number of certain hypergraphs defined by geometric regions. This problem has close relations to conflict-free colorings [4]. One of the most interesting type of regions to consider for this problem is that of the axis-parallel rectangles. We completely solve the problem for a special case of them, for bottomless rectangles. We also give an almos...
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We consider a coloring problem on dynamic, one-dimensional point sets: points appearing and disappearing on a line at given times. We wish to color them with k colors so that at any time, any sequence of p(k) consecutive points, for some function p, contains at least one point of each color. We prove that no such function p(k) exists in general. However, in the restricted case in which points a...
متن کاملColoring geometric hypergraph defined by an arrangement of half-planes
We prove that any finite set of half-planes can be colored by two colors so that every point of the plane, which belongs to at least three half-planes in the set, is covered by half-planes of both colors. This settles a problem of Keszegh.
متن کاملColoring Axis-Parallel Rectangles
For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by precisely r members of the family, all of which have the same color. For r = 2, this answers a question of S. Smorodinsky [S07].
متن کاملColoring and Maximum Independent Set of Rectangles
In this paper, we consider two geometric optimization problems: Rectangle Coloring problem (RCOL) and Maximum Independent Set of Rectangles (MISR). In RCOL, we are given a collection of n rectangles in the plane where overlapping rectangles need to be colored differently, and the goal is to find a coloring that minimizes the number of colors. Let q be the maximum clique size of the instance, i....
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2012
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2011.09.004