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Identification problems in graphs.

  • Florent Foucaud

We will introduce the audience to the topic of certain types
of identification problems in graphs such as identifying codes,
locating-dominating sets and the metric dimension. In these types of
problems, we wish to choose a subset of elements that "covers" the
graph in such a way that all elements are "identified" (i.e. uniquely
determined) by our choice. Several definitions will be considered, and
a selection of recent advances will be presented. One of the oldest
results in the area is Bondy's celebrated theorem on set systems [J.
A. Bondy. Induced subsets. Journal of Combinatorial Theory, Series B
12:201-202, 1972]. We will start by presenting it. Some algorithmic
aspects will also be addressed.