Published June 1996
| Version v1
Conference paper
Tight bounds on the size of 2-monopolies
- Others:
- Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
- Weizmann Institute of Science [Rehovot, Israël]
- French-Israeli cooperation (AFIRST)Israel Ministry of Science and Art
- Israel Science Foundation
- Carleton University
- Carleton University Press
Description
This papers deals with the question of the influence of a monopoly of vertices, seeking to gain the majority in local neighborhoods in a graph. Say that a vertex v is r-controlled by a set of vertices M if the majority of its neighbors at distance r are from M. We ask how large must M be in order to r-monopolize the graph, namely, r-control every vertex. Tight upper and lower bounds are provided for this problem. For any even ≥ 2, an r-monopoly M in an n-vertex graph must be of size Ω(n"/5), and there exist n-vertex graphs with r-monopolies of size O(n3/5).
Abstract
International audience
Additional details
- URL
- https://hal.archives-ouvertes.fr/hal-03832700
- URN
- urn:oai:HAL:hal-03832700v1
- Origin repository
- UNICA