Abstract
This paper considers the question of the influence of a coalition of vertices, seeking to gain control (or majority) in local neighborhoods in a graph. A vertex u is said to be controlled by the coalition M if the majority of its neighbors are from M. Let Ruled(G, M) denote the set of vertices controlled by M in G. Previous studies focused on constructions allowing small coalitions to control many vertices, and provided tight bounds for the maximum possible size of Ruled(G, M) (as a function of |M |). This paper introduces the dual problem, concerning the existence and construction of graphs immune to the influence of small coalitions, i.e., graphs G for which Ruled(G, M) is small (relative to |M| again) for every coalition M. Upper and lower bounds are derived on the extent to which such immunity can be achieved.
Original language | English |
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Pages (from-to) | 168-179 |
Number of pages | 12 |
Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
Volume | 8001 |
DOIs | |
State | Published - 2014 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- General Computer Science