A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Helly-Type Theorems for Line Transversals to Disjoint Unit Balls

2007
*
Discrete & Computational Geometry
*

We prove

doi:10.1007/s00454-007-9022-1
fatcat:c5ydsooky5avdm5rbgrokqfkyy
*Helly*-*type**theorems**for**line**transversals**to**disjoint**unit**balls*in R d . ... In particular, we show that a family of n ≥ 2d*disjoint**unit**balls*in R d has a*line**transversal*if,*for*some ordering ≺ of the*balls*, any subfamily of 2d*balls*admits a*line**transversal*consistent with ... Batog*for*helpful discussions on inflatability. ...##
###
A Helly-Type Theorem for Line Transversals to Disjoint Unit Balls

2003
*
Discrete & Computational Geometry
*

The proof also uses the recent result on geometric permutations

doi:10.1007/s00454-002-0793-0
fatcat:4slhx5yofvblhf5slqeubyt4gy
*for**disjoint**unit**balls*... Let F be a family of*disjoint**unit**balls*in R 3 . ... . , B n+1 }, with n ≥ n 0 being a family of n + 1*disjoint**unit**balls*in R 3 that has T (n). We shall show that F admits a*line**transversal*, which will imply*Theorem*1. ...##
###
Helly-Type Theorems for Line Transversals to Disjoint Unit Balls
[chapter]

*
Twentieth Anniversary Volume:
*

We prove

doi:10.1007/978-0-387-87363-3_12
fatcat:pchtke37are3vc53wvq3b2ofxy
*Helly*-*type**theorems**for**line**transversals**to**disjoint**unit**balls*in R d . ... In particular, we show that a family of n 2d*disjoint**unit**balls*in R d has a*line**transversal*if,*for*some ordering ≺ of the*balls*, any subfamily of 2d*balls*admits a*line**transversal*consistent with ... Batog*for*helpful discussions on inflatability. ...##
###
Some Discrete Properties of the Space of Line Transversals to Disjoint Balls
[chapter]

2009
*
IMA Volumes in Mathematics and its Applications
*

We review recent progress in the special case of

doi:10.1007/978-1-4419-0999-2_3
fatcat:snteyqtjojh6rjbeui6r4ih65m
*disjoint*Euclidean*balls*in R d , more precisely the inter-related notions of cone of directions, geometric permutations and*Helly*-*type**theorems*, and discuss ... Attempts*to*generalize Helly's*theorem**to*sets of*lines*intersecting convex sets led*to*a series of results relating the geometry of a family of sets in R d*to*the structure of the space of*lines*intersecting ... The author is grateful*to*Boris Aronov, Ciprian Borcea, Otfried Cheong, Olivier Devillers, Hazel Everett, Andreas Holmsen and Sylvain Petitjean*for*helpful discussions. ...##
###
Hadwiger and Helly-type theorems for disjoint unit spheres
[article]

2007
*
arXiv
*
pre-print

We prove

arXiv:cs/0702039v1
fatcat:fut5f2ced5c3dnohtiuxvag4ya
*Helly*-*type**theorems**for**line**transversals**to**disjoint**unit**balls*in ^d. ... In particular, we show that a family of n ≥ 2d*disjoint**unit**balls*in ^d has a*line**transversal*if,*for*some ordering ≺ of the*balls*, any subfamily of 2d*balls*admits a*line**transversal*consistent with ... Batog*for*helpful discussions on inflatability. ...##
###
A Helly-Type Theorem for Hyperplane Transversals to Well-Separated Convex Sets

2001
*
Discrete & Computational Geometry
*

This is the first

doi:10.1007/s00454-001-0016-0
fatcat:g2kfdrh5zreufmjepqha6zxbgu
*Helly*-*type**theorem*known*for*hyperplane*transversals**to*compact convex sets of arbitrary shape in dimension greater than one. ... We say that the collection S is ε-separated if,*for*every 0 < k < d, any k of the sets can be separated from any other d − k of the sets by a hyperplane more than ε D(S)/2 away from all d of the sets. ...*For*d = 2, our result yields a*Helly*-*type**theorem**for**line**transversals**to*ε-separated collections of pairwise*disjoint*convex sets in R 2 . ...##
###
The Harmony of Spheres

2007
*
Canadian Conference on Computational Geometry
*

(

dblp:conf/cccg/Cheong07
fatcat:7limp2lwhjffbettbtgg7jigya
*For*4 ≥ n ≥ 8, it is still open whether the correct answer is two or three.) The first*Helly*-*type**theorem**for**line**transversals**to*spheres was proven by Holmsen et al. [4] . ... In this talk we discuss recent results on*transversals**to**disjoint*spheres (*balls*) in three and more dimensions. Katchalski et al. ...##
###
Lower Bounds for Pinning Lines by Balls (Extended Abstract)

2009
*
Electronic Notes in Discrete Mathematics
*

We show that the constant 2d is best possible, in any dimension, and derive lower bounds on

doi:10.1016/j.endm.2009.07.094
fatcat:phwmwb5j2rf6rpm4jnh4oejfhi
*Helly*numbers*for*sets of*line**transversals**to**disjoint**balls*in arbitrary dimension. ... It is known that if n ≥ 2d pairwise*disjoint**balls*in R d have a unique*line*intersecting them in a given order ≺, one can always remove a*ball*so that remains the only*line*intersecting the*balls*in the ... The corresponding*Helly*number,*for**transversals**to**disjoint**unit**balls*in R d , is known*to*be between 5 and 4d − 1. ...##
###
Discrete and Lexicographic Helly-Type Theorems

2007
*
Discrete & Computational Geometry
*

We define three new

doi:10.1007/s00454-007-9028-8
fatcat:xfxzbfvfbzdbbeactazvek5jda
*types*of*Helly**theorems*: discrete*Helly**theorems*-where the common point should belong*to*an a-priori given set, lexicographic*Helly**theorems*-where the common point should not be lexicographically ... We study the relations between the different*types*of the*Helly**theorems*. We obtain several new discrete and lexicographic*Helly*numbers. ... Acknowledgements The author would like*to*thank Branko Grünbaum*for*inspiring discussions and an anonymous referee*for*many useful comments which greatly improved the presentation of this paper. ...##
###
The Katchalski-Lewis Transversal Problem in Rn

2007
*
Discrete & Computational Geometry
*

Also we give two constructions of families of pairwise

doi:10.1007/s00454-006-1291-6
fatcat:bmpbwhmlabe4vfetglrskmmrgm
*disjoint*translates of the*unit**ball*in R 3 which answer some related questions. * Supported by the Research Council of Norway. 342 A. Holmsen ...*line*. ... Acknowledgments Special thanks*to*Boris Aronov*for*many helpful discussions. Also the construction of Proposition 7 was found independently by B. Aronov, V. Koltun, and M. Sharir. ...##
###
Line Transversals to Unit Disks

2002
*
Discrete & Computational Geometry
*

We show that if every three members of a finite

doi:10.1007/s00454-002-2821-5
fatcat:efqfo42ykbbyxgaaqxggdy374y
*disjoint*family of*unit*disks in the plane have a*line**transversal*, then there is a*line**transversal**to*all except at most 12 disks in the family. ... We derive an analogous result*for*translates of a general compact convex set, with the constant equal*to*47. ... Acknowledgments I am indebted*to*Boris Aronov, Wlodek Kuperberg and two anonymous referees whose comments were helpful in improving both the results and the presentation of this paper. ...##
###
No Helly Theorem for Stabbing Translates by Lines in R 3

2004
*
Discrete & Computational Geometry
*

*For*each n > 2 we construct a convex body K ⊂ R 3 and a finite family F of

*disjoint*translates of K such that any n − 1 members F admit a

*line*

*transversal*, but F has no

*line*

*transversal*. ... [6] shows that there is a finite

*Helly*number 406 A. Holmsen and J. Matoušek

*for*

*line*

*transversals*

*to*families of

*disjoint*

*unit*

*balls*in R 3 . ... There is no Hadwiger-

*type*

*theorem*

*for*

*line*

*transversals*

*to*families of

*disjoint*translates in R 3 . 3. ...

##
###
A Helly-type theorem for higher-dimensional transversals

2002
*
Computational geometry
*

It is the first

doi:10.1016/s0925-7721(01)00025-6
fatcat:odkjicyzercupizvhyk4fgz2hu
*Helly*-*type**theorem*known*for**transversals*of dimension between 1 and d − 1. ... This result generalizes a*theorem*of Hadwiger(-Danzer-Grünbaum-Klee) on*line**transversals**for*an unbounded family of compact convex sets. ... of*Helly**type*were found*for*both*line**transversals*and hyperplane*transversals**to*collections restricted by size or shape, such as*unit**balls*, parallelepipeds, translates of a single convex body, etc ...##
###
Page 2227 of Mathematical Reviews Vol. , Issue 2004c
[page]

2004
*
Mathematical Reviews
*

*disjoint*

*unit*

*balls*. ... Carla Peri (l-SACM-GM,; Milan) 2004¢:52010 52A35 Holmsen, Andreas (N-BERG; Bergen) ; Katchalski, Meir (IL-TECHM; Haifa); Lewis, Ted (3-AB-MS; Edmonton, AB) A

*Helly*-

*type*

*theorem*

*for*

*line*

*transversals*

*to*...

##
###
Helly-Type Theorems and Geometric Transversals
[chapter]

2004
*
Handbook of Discrete and Computational Geometry, Second Edition
*

HADWIGER'S

doi:10.1201/9781420035315.ch4
fatcat:x3epiiq2kbf6nenkswsfaqmsdi
*TRANSVERSAL**THEOREM*In 1935, Vincensini asked if there is a*Helly*-*type**theorem**for**line**transversals**to*a family A of convex sets in R 2 . ... CONVEXITY ON THE AFFINE GRASSMANNIAN There is no*Helly*-*type**theorem**for*convex sets of kats in R d since such a*theorem*would be equivalent*to*a*Helly*-*type**theorem**for*k-*transversals*in R d . ...
« Previous

*Showing results 1 — 15 out of 92 results*