The strip of minimum width covering a centrally symmetric set of points

Huicochea, Mario; Jerónimo-Castro, Jesús

doi:10.1007/s10998-009-9047-7

Cited by 5 publications

(2 citation statements)

References 9 publications

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“…Furthermore, let μ(K) be the supremum of the K-widths of the parallelograms with the T K (3) property. It is known that μ(B) = √ 2 (to see [3] and [7]), however, for an arbitrary convex body K we have the following.…”

Section: Lemmamentioning

confidence: 99%

Line Transversals to Translates of a Convex Body

Jerónimo-Castro

Roldán-Pensado²

2010

Discrete Comput Geom

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Let K be a convex body in the plane. Define λ(K, t) as the smallest number satisfying the following: if F is any family of translates of K such that every t members of F have a common transversal, then all the members of λ(K, t)F have a common transversal. We give bounds for λ(K, 3) and λ(K, 4) for a general convex figure K. In particular, we obtain that λ(K, 3) ≤ 1.79 when K is the Euclidean disc.

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Section: Lemmamentioning

confidence: 99%

Line Transversals to Translates of a Convex Body

Jerónimo-Castro

Roldán-Pensado²

2010

Discrete Comput Geom

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“…There are some results about the minimum λ for families of translates of the unit disc in the plane (for instance [1][2][3][4][5]). However, as far as we know, there is no published result about λ d (k) for families of non congruent balls.…”

Section: Introductionmentioning

confidence: 99%

Line transversals to blown up closed balls

Jerónimo-Castro

Roldán-Pensado

2011

J. Geom.

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The number λ d (k) is defined as the minimum λ > 0 such that the following holds: For any finite family F = {B1, B2, . . . , Bn} of closed balls in R d such that every k elements of F have a common line transversal, the elements of the blown up family λF = {λB1, λB2, . . . , λBn} have a common line transversal. In this paper we show that λ d (d+1) ≤ 4, λ2(4) ≤ 2 √ 2 and λ2(3) < 2.88. Mathematics Subject Classification (2010). 52A35.

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Problems in Discrete Geometry

Eckhoff

2016

Convexity and Discrete Geometry Including Graph Theory

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The strip of minimum width covering a centrally symmetric set of points

Cited by 5 publications

References 9 publications

Line Transversals to Translates of a Convex Body

Line Transversals to Translates of a Convex Body

Line transversals to blown up closed balls

Problems in Discrete Geometry

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