# Contagious Sets in Dense Graphs

@article{Freund2015ContagiousSI, title={Contagious Sets in Dense Graphs}, author={Daniel Freund and Matthias Poloczek and Daniel Reichman}, journal={ArXiv}, year={2015}, volume={abs/1503.00158} }

We study the activation process in undirected graphs known as bootstrap percolation: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it had at least r active neighbors, for a threshold r that is identical for all vertices. A contagious set is a vertex set whose activation results with the entire graph being active. Let m(G,r) be the size of a smallest contagious set in a graph G on n vertices.
We examine density conditions that ensure m(G,r… CONTINUE READING

#### Topics from this paper.

#### Citations

##### Publications citing this paper.

SHOWING 1-9 OF 9 CITATIONS

## Extremal graph theory via structural analysis

VIEW 1 EXCERPT

CITES BACKGROUND

## Contagious sets in a degree-proportional bootstrap percolation process

VIEW 1 EXCERPT

CITES METHODS

## Minimum degree conditions for small percolating sets in bootstrap percolation

VIEW 13 EXCERPTS

CITES BACKGROUND, METHODS & RESULTS

HIGHLY INFLUENCED

## Evangelism in Social Networks: Algorithms and Complexity

VIEW 1 EXCERPT

CITES RESULTS

## Whom to Befriend to Influence People

VIEW 1 EXCERPT

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 11 REFERENCES

## Contagious Sets in Expanders

VIEW 1 EXCERPT

## New bounds for contagious sets

VIEW 2 EXCERPTS

## Bootstrap percolation on the random regular graph

VIEW 1 EXCERPT

## Majority bootstrap percolation on the random graph G(n,p)

VIEW 2 EXCERPTS

## Combinatorial model and bounds for target set selection

VIEW 2 EXCERPTS

## Bootstrap percolation on the hypercube

VIEW 1 EXCERPT

## Bootstrap percolation on a Bethe lattice

VIEW 1 EXCERPT