The power of small coalitions in graphs

J. C. Bermond; J. Bond; D. Peleg; S. Perennes

doi:10.1016/S0166-218X(02)00241-X

The power of small coalitions in graphs

J. C. Bermond, J. Bond, D. Peleg, S. Perennes

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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 general graph. Say that a vertex v is controlled by the coalition M if the majority of its neighbors are from M. We ask how many vertices (as a function of |M|) can M control in this fashion. Upper and lower bounds are provided for this problem, as well as for cases where the majority is computed over larger neighborhoods (either neighborhoods of some fixed radius r > 1, or all neighborhoods of radii up to r). In particular, we look also at the case where the coalition must control all vertices (including or excluding its own), and derive bounds for its size.

Original language	English
Pages (from-to)	399-414
Number of pages	16
Journal	Discrete Applied Mathematics
Volume	127
Issue number	3
DOIs	https://doi.org/10.1016/S0166-218X(02)00241-X
State	Published - 1 May 2003
Externally published	Yes

Bibliographical note

Funding Information:
This work was partly supported by a grant from AFIRST and the Israel Ministry of Science and Arts (in the framework of the French–Israeli cooperation). Parts of this paper have appeared in preliminary form in [2,3] .

Funding

This work was partly supported by a grant from AFIRST and the Israel Ministry of Science and Arts (in the framework of the French–Israeli cooperation). Parts of this paper have appeared in preliminary form in [2,3] .

Funders	Funder number
AFIRST
Israel Ministry of Science and Arts

Access to Document

10.1016/S0166-218X(02)00241-X

Cite this

@article{8543cef0b4124b5ab76261308c6a2cac,

title = "The power of small coalitions in graphs",

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 general graph. Say that a vertex v is controlled by the coalition M if the majority of its neighbors are from M. We ask how many vertices (as a function of |M|) can M control in this fashion. Upper and lower bounds are provided for this problem, as well as for cases where the majority is computed over larger neighborhoods (either neighborhoods of some fixed radius r > 1, or all neighborhoods of radii up to r). In particular, we look also at the case where the coalition must control all vertices (including or excluding its own), and derive bounds for its size.",

author = "Bermond, {J. C.} and J. Bond and D. Peleg and S. Perennes",

note = "Funding Information: This work was partly supported by a grant from AFIRST and the Israel Ministry of Science and Arts (in the framework of the French–Israeli cooperation). Parts of this paper have appeared in preliminary form in [2,3] . ",

year = "2003",

month = may,

day = "1",

doi = "10.1016/S0166-218X(02)00241-X",

language = "אנגלית",

volume = "127",

pages = "399--414",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier B.V.",

number = "3",

}

TY - JOUR

T1 - The power of small coalitions in graphs

AU - Bermond, J. C.

AU - Bond, J.

AU - Peleg, D.

AU - Perennes, S.

N1 - Funding Information: This work was partly supported by a grant from AFIRST and the Israel Ministry of Science and Arts (in the framework of the French–Israeli cooperation). Parts of this paper have appeared in preliminary form in [2,3] .

PY - 2003/5/1

Y1 - 2003/5/1

N2 - This paper considers the question of the influence of a coalition of vertices, seeking to gain control (or majority) in local neighborhoods in a general graph. Say that a vertex v is controlled by the coalition M if the majority of its neighbors are from M. We ask how many vertices (as a function of |M|) can M control in this fashion. Upper and lower bounds are provided for this problem, as well as for cases where the majority is computed over larger neighborhoods (either neighborhoods of some fixed radius r > 1, or all neighborhoods of radii up to r). In particular, we look also at the case where the coalition must control all vertices (including or excluding its own), and derive bounds for its size.

AB - This paper considers the question of the influence of a coalition of vertices, seeking to gain control (or majority) in local neighborhoods in a general graph. Say that a vertex v is controlled by the coalition M if the majority of its neighbors are from M. We ask how many vertices (as a function of |M|) can M control in this fashion. Upper and lower bounds are provided for this problem, as well as for cases where the majority is computed over larger neighborhoods (either neighborhoods of some fixed radius r > 1, or all neighborhoods of radii up to r). In particular, we look also at the case where the coalition must control all vertices (including or excluding its own), and derive bounds for its size.

UR - http://www.scopus.com/inward/record.url?scp=84867959143&partnerID=8YFLogxK

U2 - 10.1016/S0166-218X(02)00241-X

DO - 10.1016/S0166-218X(02)00241-X

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84867959143

SN - 0166-218X

VL - 127

SP - 399

EP - 414

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 3

ER -

The power of small coalitions in graphs

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this