Offensive alliances in graphs
نویسندگان
چکیده
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.
منابع مشابه
Global Offensive Alliances in Graphs via Degree Sequences
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متن کاملGlobal O ensive Alliances in Graphs via Degree Sequences
A global offensive alliance in a graph G = (V,E) is a subset S of V such that for every vertex v not in S at least half of the vertices in the closed neighborhood of v are in S. We give an upper bound on the global offensive alliance number of a graph in terms of its degree sequence. We also study global offensive alliances of random graphs.
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ورودعنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 24 شماره
صفحات -
تاریخ انتشار 2004