Lower Bounds for Pinning Lines by Balls (Extended Abstract)

Abstract : It is known that if n>=2d pairwise disjoint balls in R^d have a unique line ℓ intersecting them in a given order <, one can always remove a ball so that ℓ remains the only line intersecting the balls in the order induced by <. We show that the constant 2d is best possible, in any dimension, and derive lower bounds on Helly numbers for sets of line transversals to disjoint balls in arbitrary dimension.
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Communication dans un congrès
European Conference on Combinatorics, Graph Theory and Applications - EuroComb 2009, Sep 2009, Bordeaux, France. Elsevier, 34, pp.567-571, 2009, Electronic Notes in Discrete Mathematics (ENDM). 〈http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B75GV-4WWHRTR-3C&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=79af951d447239bd59b51c623ade6428〉. 〈10.1016/j.endm.2009.07.094〉
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Otfried Cheong, Xavier Goaoc, Andreas Holmsen. Lower Bounds for Pinning Lines by Balls (Extended Abstract). European Conference on Combinatorics, Graph Theory and Applications - EuroComb 2009, Sep 2009, Bordeaux, France. Elsevier, 34, pp.567-571, 2009, Electronic Notes in Discrete Mathematics (ENDM). 〈http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B75GV-4WWHRTR-3C&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=79af951d447239bd59b51c623ade6428〉. 〈10.1016/j.endm.2009.07.094〉. 〈inria-00431437〉

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