TY - UNPB
T1 - Dynamic Monopolies in Reversible Bootstrap Percolation
AU - Jeger, Clemens
AU - Zehmakan, Ahad N.
N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2018
Y1 - 2018
N2 - We study an extremal question for the (reversible) r−bootstrap percolation processes. Given a graph and an initial configuration where each vertex is active or inactive, in the r−bootstrap percolation process the following rule is applied in discrete-time rounds: each vertex gets active if it has at least r active neighbors, and an active vertex stays active forever. In the reversible r-bootstrap percolation, each vertex gets active if it has at least r active neighbors, and inactive otherwise. We consider the following question on the d-dimensional torus: how many vertices should be initially active so that the whole graph becomes active? Our results settle an open problem by Balister, Bollobás, Johnson, and Walters and generalize the results by Flocchini, Lodi, Luccio, Pagli, and Santoro.
AB - We study an extremal question for the (reversible) r−bootstrap percolation processes. Given a graph and an initial configuration where each vertex is active or inactive, in the r−bootstrap percolation process the following rule is applied in discrete-time rounds: each vertex gets active if it has at least r active neighbors, and an active vertex stays active forever. In the reversible r-bootstrap percolation, each vertex gets active if it has at least r active neighbors, and inactive otherwise. We consider the following question on the d-dimensional torus: how many vertices should be initially active so that the whole graph becomes active? Our results settle an open problem by Balister, Bollobás, Johnson, and Walters and generalize the results by Flocchini, Lodi, Luccio, Pagli, and Santoro.
M3 - Working paper
BT - Dynamic Monopolies in Reversible Bootstrap Percolation
ER -