scholarly journals Ore and Chvátal‐type degree conditions for bootstrap percolation from small sets

2020 ◽  
Vol 94 (2) ◽  
pp. 252-266 ◽  
Author(s):  
Michael Dairyko ◽  
Michael Ferrara ◽  
Bernard Lidický ◽  
Ryan R. Martin ◽  
Florian Pfender ◽  
...  
Keyword(s):  
Bootstrap Percolation ◽  
Degree Conditions

scholarly journals Minimum Degree Conditions for Small Percolating Sets in Bootstrap Percolation

10.37236/6937 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Karen Gunderson
Keyword(s):  
Minimum Degree ◽  
Bootstrap Percolation ◽  
Sharp Condition ◽  
Large Graph ◽  
Degree Conditions

The $r$-neighbour bootstrap process is an update rule for the states of vertices in which `uninfected' vertices with at least $r$ `infected' neighbours become infected and a set of initially infected vertices is said to percolate if eventually all vertices are infected.  For every $r \geq 3$, a sharp condition is given for the minimum degree of a sufficiently large graph that guarantees the existence of a percolating set of size $r$.  In the case $r=3$, for $n$ large enough, any graph on $n$ vertices with minimum degree $\lfloor n/2 \rfloor +1$ has a percolating set of size $3$ and for $r \geq 4$ and $n$ large enough (in terms of $r$), every graph on $n$ vertices with minimum degree $\lfloor n/2 \rfloor + (r-3)$ has a percolating set of size $r$.  A class of examples are given to show the sharpness of these results.

Transport through bootstrap percolation clusters

1991 ◽  
Vol 1 (5) ◽  
pp. 685-692 ◽  
Author(s):  
Muhammad Sahimi ◽  
Tane S. Ray
Keyword(s):  
Bootstrap Percolation ◽  
Percolation Clusters

Comparison of bootstrap percolation models

1989 ◽  
Vol 22 (7) ◽  
pp. L297-L301 ◽  
Author(s):  
J Adler ◽  
D Stauffer ◽  
A Aharony
Keyword(s):  
Bootstrap Percolation

Bootstrap percolation on certain branching media

1983 ◽  
Vol 16 (32) ◽  
pp. 6263-6274 ◽  
Author(s):  
Y S Yang ◽  
Z Q Zhang
Keyword(s):  
Bootstrap Percolation

scholarly journals Bootstrap Percolation on a Graph with Random and Local Connections

2015 ◽  
Vol 160 (5) ◽  
pp. 1249-1276 ◽  
Author(s):  
Tatyana S. Turova ◽  
Thomas Vallier
Keyword(s):  
Bootstrap Percolation

scholarly journals THRESHOLD VALUE OF THREE-DIMENSIONAL BOOTSTRAP PERCOLATION

2003 ◽  
Vol 14 (04) ◽  
pp. 529-536 ◽  
Author(s):  
DIRK KURTSIEFER
Keyword(s):  
Present Article ◽  
Three Dimensional ◽  
Threshold Value ◽  
Critical Value ◽  
Bootstrap Percolation ◽  
Infinite Lattice

The present article deals with the critical value pc of the three-dimensional bootstrap percolation. We will check the behavior of pc for different lengths of the lattice and additionally we will scale pc in the limit of an infinite lattice.

scholarly journals Extremal Bounds for Bootstrap Percolation in the Hypercube

2017 ◽  
Vol 61 ◽  
pp. 877-883
Author(s):  
Natasha Morrison ◽  
Jonathan A. Noel
Keyword(s):  
Bootstrap Percolation
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