منابع مشابه
A Note about Bezdek's Conjecture on Covering an Annulus by Strips
A closed plane region between two parallel lines is called a strip. András Bezdek posed the following conjecture: For each convex region K there is an ε > 0 such that if εK lies in the interior of K and the annulus K\εK is covered by finitely many strips, then the sum of the widths of the strips must be at least the minimal width of K. In this paper, we consider problems which are related to th...
متن کاملCovering Polygonal Annuli by Strips
In 2000 A. Bezdek asked which plane convex bodies have the property that whenever an annulus, consisting of the body less a sufficiently small scaled copy of itself, is covered by strips, the sum of the widths of the strips must still be at least the minimal width of the body. We characterise the polygons for which this is so. In this note we will give a complete answer for convex polygons to t...
متن کاملON COVERING POINTS WITH CONICS AND STRIPS IN THE PLANE A Thesis by PRAVEEN TIWARI
Geometric covering problems have always been of focus in computer scientific research. The generic geometric covering problem asks to cover a set S of n objects with another set of objects whose cardinality is minimum, in a geometric setting. Many versions of geometric cover have been studied in detail, one of which is line cover: Given a set of points in the plane, find the minimum number of l...
متن کاملAn Algebraic Annulus Theorem
This result has also been proved by Bowditch [2], using very different methods. We discuss these differences at the end of this introduction. The terminology used is standard (from [11] and [17]). The importance of splitting groups along infinite cyclic subgroups is well known from the work of Paulin [13], Rips and Sela [14] and Sela [18]. If G has an infinite cyclic subgroup H such that e(G,H)...
متن کاملCovering triples by quadruples: An asymptotic solution
Let C(3,4, n) be the minimum number of four-element subsets (called blocks) of an n-element set, X, such that each three-element subset of X is contained in at least one block. Let L(3,4, n) = rn/4rn 1/3rn 2/2111. Schoenheim has shown that C(3,4, n) 2 L(3,4, n). The construction of Steiner quadruple systems of all orders n ~2 or 4 (mod 6) by Hanani (Canad. J. Math. 12 (1960), 145-157) can be us...
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ژورنال
عنوان ژورنال: Discrete and Computational Geometry
سال: 2003
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-003-0002-y