Indecomposable Coverings

被引：14
|
作者：
Pach, Janos [1 ,2 ]
Tardos, Gabor [3 ]
Toth, Geza [4 ]
机构：
[1] CUNY City Coll, New York, NY 10012 USA
[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA
[3] Simon Fraser Univ, Sch Comp Sci, Burnaby, BC V5A 1S6, Canada
[4] Hungarian Acad Sci, Renyi Inst, H-1364 Budapest, Hungary
来源：
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2009年 / 52卷 / 03期
基金：
加拿大自然科学与工程研究理事会; 美国国家科学基金会;
关键词：
PLANE;
D O I：
10.4153/CMB-2009-048-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that for every k > 1, there exist k-fold coverings of the plane (i) with strips, 00 with axis-parallel rectangles, and (iii) with homothets of any fixed concave quadrilateral, that cannot be decomposed in to two coverings. We also construct for every k > 1 a set of points P and a family of disks D in the plane, each containing at least k elements of P, such that, no matter how we color the points of P with two colors, there exists a disk D is an element of D all of whose points are of the same color.
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页码：451 / 463
页数：13
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