#### (équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 05 décembre //20 à 13h45 en B311, Bernard Ries nous parlera de : **Why some vertices/edges are more important than others***Résumé :* Problems of safety and reliability occur in many practical
contexts and adequate formulations of such issues have opened the way
to possible treatments by mathematical optimization procedures. It is
in particular the case in situations where a complex system has to be
protected against attacks and for this purpose one may have to
identify the “most important” elements of the system. To be concrete,
assume we have a finite system S (collection of components) which can
be operated in different ways. Each operating mode s is characterized
by the subsets of components it uses. In order to find the most
important components of S we may want to identify a smallest possible
subset T of components in S which is such that every operating mode s
has at least d components in T. In this talk, I will present results
concerning several cases where S is a (weighted) graph and each
operating mode s is associated with a combinatorial structure like for
instance a matching, or a stable set, or a vertex cover, etc.