Eliminating cycles in the discrete torus

Béla Bollobás*, Guy Kindler, Imre Leader, Ryan O'Donnell

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


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.

Original languageAmerican English
Title of host publicationLATIN 2006
Subtitle of host publicationTheoretical Informatics - 7th Latin American Symposium, Proceedings
PublisherSpringer Verlag
Number of pages9
ISBN (Print)354032755X, 9783540327554
StatePublished - 2006
Externally publishedYes
EventLATIN 2006: Theoretical Informatics - 7th Latin American Symposium - Valdivia, Chile
Duration: 20 Mar 200624 Mar 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3887 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceLATIN 2006: Theoretical Informatics - 7th Latin American Symposium


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