@inproceedings{d8c68a94ba7f4629accd5d49b22ec032,

title = "Eliminating cycles in the discrete torus",

abstract = "In this paper we consider the following question: how many vertices of the discrete torus must be deleted so that no topologically nontrivial cycles remain? We look at two different edge structures for the discrete torus. For (ℤmd)1, where two vertices in ℤm are connected if their l1 distance is 1, we show a nontrivial upper bound of dlog2(3/2)md-1 ≈ d 0.6md-1 on the number of vertices that must be deleted. For (ℤmd)∞ where two vertices are connected if their l∞ distance is 1, Saks, Samorodnitsky and Zosin [8] already gave a nearly tight lower bound of d(m - 1)d-1 using arguments involving linear algebra. We give a more elementary proof which improves the bound to md - (m - 1)d, which is precisely tight.",

author = "B{\'e}la Bollob{\'a}s and Guy Kindler and Imre Leader and Ryan O'Donnell",

year = "2006",

doi = "10.1007/11682462_22",

language = "American English",

isbn = "354032755X",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "202--210",

booktitle = "LATIN 2006",

address = "Germany",

note = "LATIN 2006: Theoretical Informatics - 7th Latin American Symposium ; Conference date: 20-03-2006 Through 24-03-2006",

}