DeepAI AI Chat
Log In Sign Up

Dynamic monopolies for interval graphs with bounded thresholds

by   Stéphane Bessy, et al.

For a graph G and an integer-valued threshold function τ on its vertex set, a dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ(u) neighbors in it eventually yields the vertex set of G. We show that the problem of finding a dynamic monopoly of minimum order can be solved in polynomial time for interval graphs with bounded threshold functions, but is NP-hard for chordal graphs allowing unbounded threshold functions.


page 1

page 2

page 3

page 4


On some tractable and hard instances for partial incentives and target set selection

A widely studied model for influence diffusion in social networks are t...

Prophet Inequalities on the Intersection of a Matroid and a Graph

We consider prophet inequalities in a setting where agents correspond to...

Non-monotone target sets for threshold values restricted to 0, 1, and the vertex degree

We consider a non-monotone activation process (X_t)_t∈{ 0,1,2,…} on a gr...

Degree Sequence Optimization in Bounded Treewidth

We consider the problem of finding a subgraph of a given graph which min...

Cortical Computation via Iterative Constructions

We study Boolean functions of an arbitrary number of input variables tha...

On Degree Sequence Optimization

We consider the problem of finding a subgraph of a given graph which max...

Defensive Domination in Proper Interval Graphs

k-defensive domination, a variant of the classical domination problem on...