Space coverings by translates of convex sets
نویسندگان
چکیده
منابع مشابه
The Star Number of Coverings of Space with Convex Bodies
1. When a system of sets covers a space, the star number of the covering is the supremum over the sets of the system of the cardinals of the numbers of sets of the system meeting a set of the system . The standard Lebesgue 'brick-laying' construction provides an example, for each positive integer n, of a lattice covering of R" by closed rectangular parallelepipeds with star number 2"T'-1 . In v...
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We show that the visibility graph of a set of non-intersecting translates of the same compact convex object in R always contains a Hamiltonian path. Furthermore, we show that every other edge in the Hamiltonian path can be used to obtain a perfect matching that is realized by a set of non-intersecting lines of sight. ? 2001 Elsevier Science B.V. All rights reserved.
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We introduce and study t-coverings in En, i.e., arrangements of proper translates of a convex body K ⊂ En sufficient to cover K. First, we investigate relations between t-coverings of the whole of K and t-coverings of its boundary only. Refining the notion of t-covering in several ways, we then derive, particularly for centrally symmetric convex bodies and n = 2, theorems which are interesting ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1979
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1979.82.379