# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

## OFFENSIVE ALLIANCES IN GRAPHS

Odile Favaron1, Gerd Fricke2, Wayne Goddard3,4, Sandra M. Hedetniemi4, Stephen T. Hedetniemi4, Petter Kristiansen5, Renu C. Laskar4 and R. Duane Skaggs2

1Université Paris-Sud, 2Morehead State University, 3University of KwaZulu-Natal, Durban, 4Clemson University and 5University of Bergen

## Abstract

A set S is an offensive alliance if for every vertex v in its boundary N(S)− S it holds that the majority of vertices in v's closed neighbourhood are in S. The offensive alliance number is the minimum cardinality of an offensive alliance. In this paper we explore the bounds on the offensive alliance and the strong offensive alliance numbers (where a strict majority is required). In particular, we show that the offensive alliance number is at most 2/3 the order and the strong offensive alliance number is at most 5/6 the order.

Keywords: alliance, offensive, majority, graph.

2000 Mathematics Subject Classification: 05C90, 05C69.

## References

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