Odile Favaron

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A vertex x in a subset X of vertices of an undirected graph is dm.dant if its closed neighbourhowl is contained in the union c\f closed neigl&ourh&s of vertices o F X--(x}. In tI;e context of a communications network, this means that any vertw which may rexive cornmunications from X may also be informed from X-(x). The lower tend upper incdu +&wee aumbers(More)
A graph is said to be k-factor-critical if the removal of any set of k vertices results in a graph with a perfect matching. We study some properties of k-factor-critical graphs and show that many results on q-extendable graphs can be improved using this concept.
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(More)