Size bounds for dynamic monopolies
Discrete Applied Mathematics
Optimal irreversible dynamos in chordal rings
Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
Dynamic monopolies of constant size
Journal of Combinatorial Theory Series B
Majority Consensus and the Local Majority Rule
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
Listen to Your Neighbors: How (Not) to Reach a Consensus
SIAM Journal on Discrete Mathematics
Discrete Applied Mathematics
Note: Combinatorial model and bounds for target set selection
Theoretical Computer Science
Dynamic monopolies and feedback vertex sets in hexagonal grids
Computers & Mathematics with Applications
Bounding the number of tolerable faults in majority-based systems
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Dynamic monopolies and feedback vertex sets in hexagonal grids
Computers & Mathematics with Applications
Bounding the sizes of dynamic monopolies and convergent sets for threshold-based cascades
Theoretical Computer Science
Generalized degeneracy, dynamic monopolies and maximum degenerate subgraphs
Discrete Applied Mathematics
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In a graph theoretical model of the spread of fault in distributed computing and communication networks, each element in the network is represented by a vertex of a graph where edges connect pairs of communicating elements, and each colored vertex corresponds to a faulty element at discrete time periods. Majority-based systems have been used to model the spread of fault to a certain vertex by checking for faults within a majority of its neighbors. Our focus is on irreversible majority processes wherein a vertex becomes permanently colored in a certain time period if at least half of its neighbors were in the colored state in the previous time period. We study such processes on planar, cylindrical, and toroidal triangular grid graphs. More specifically, we provide bounds for the minimum number of vertices in a dynamic monopoly defined as a set of vertices that, if initially colored, will result in the entire graph becoming colored in a finite number of time periods.