Abstract The Weighted Safe Set Problem aims to determine in an undirected graph a subset
of vertices such that the weights of the connected components they induce exceed the …

Abstract The Weighted Safe Set Problem requires to partition an undirected graph into two
families of connected components, respectively denoted as safe and unsafe, in such a way …

Given a connected graph G=(V, E), a Safe Set S is a subset of the vertex set V such that the
cardinality of each connected component in the subgraph induced by V∖ S does not exceed …

Abstract The Safe Set Problem is a type of partitioning problem with particular constraints on
the weight of adjacent partition components. Several theoretical results exist in the literature …

The robustness of the networks is their capacity to remain operational in the presence of
faults and disruptions, and thereby it is an important tool to provide data transmission in …

Given a connected graph G=(V, E), a Safe Set S is a subset of the vertex set V such that the
cardinality of each connected component in the subgraph induced by V\S does not exceed …

For a connected simple graph G, a nonempty subset S of VG is a connected safe set if the
induced subgraph GS is connected and the inequality S≥ D satisfies for each connected …

In this thesis, we explore optimisation problems related to security, focusing on real-world
systems that can be modelled using graphs or binary matrices. The first problem we …

The Weighted Safe Set Problem requires to partition an undirected graph into two families of
connected components, respectively denoted as safe and unsafe, in such a way that each …

A connected collection of nodes in a network excluding which results in the decomposition
of a network into components such that the cardinality of each component is at most equal to …