Global alliances in planar graphs

J. A. Rodríguez-VelázquezDepartment of Computer Engineering and Mathematics Rovira i Virgili University of Tarragona Av. Països Catalans 26, 43007Tarragona, Spain e-mail: [email protected]

J. M. SigarretaDepartamento de Matemáticas Carlos III University of Madrid Avda. de la Universidad 30, 28911 Legans (Madrid), Spain e-mail: [email protected]

Odile Favaron

(Communicated by)

Abstract

In this paper we study mathematical properties of alliances (defensive alliances, offensive alliances and dual alliances) in planar graphs. In particular, we obtain several tight bounds on different types of alliance numbers of a planar graph.

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