Almost exact minimum feedback vertex set in meshes and butterflies
Information Processing Letters
Size bounds for dynamic monopolies
Discrete Applied Mathematics
Feedback vertex set in hypercubes
Information Processing Letters
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)
Minimum feedback vertex set and acyclic coloring
Information Processing Letters
New bounds on the size of the minimum feedback vertex set in meshes and butterflies
Information Processing Letters
Local majorities, coalitions and monopolies in graphs: a review
Theoretical Computer Science
Information Processing Letters
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
On time versus size for monotone dynamic monopolies in regular topologies
Journal of Discrete Algorithms
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
Discrete Applied Mathematics
Note: Combinatorial model and bounds for target set selection
Theoretical Computer Science
Bounding the number of tolerable faults in majority-based systems
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Discrete Applied Mathematics
Discrete Applied Mathematics
Bounding the sizes of dynamic monopolies and convergent sets for threshold-based cascades
Theoretical Computer Science
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In a majority conversion process, the vertices of a graph can be in one of the two states, colored or uncolored, and these states are dynamically updated so that a vertex becomes colored at a certain time period if at least half of its neighbors were in the colored state in the previous time period. A dynamic monopoly is a set of vertices in a graph that when initially colored will eventually cause all vertices in the graph to become colored. This paper establishes a connection between dynamic monopolies and the well-known feedback vertex sets which are sets of vertices whose removal results in an acyclic graph. More specifically, we show that dynamic monopolies and feedback vertex sets are equivalent in graphs wherein all vertices have degree 2 or 3. We use this equivalence to provide exact values for the minimum size of dynamic monopolies of planar hexagonal grids, as well as upper and lower bounds on the minimum size of dynamic monopolies of cylindrical and toroidal hexagonal grids. For these last two topologies, the respective upper and lower bounds differ by at most one.