Mutual visibility is a recently introduced notion motivated by shortest-path visibility in graphs. Given a connected graph $G$ and a vertex subset $\chi$,  two vertices $u$ and $v$ are $\chi$-visible if there exists a shortest $u,v$-path  whose internal vertices avoid $\chi$. A set in which every pair of vertices  is $\chi$-visible is called a mutual-visibility set, and the maximum size  of such a set is the mutual-visibility number of $G$.

Several variants of this concept have been introduced, including the total,  outer, and dual mutual-visibility parameters, each imposing different visibility  requirements on vertices inside or outside the chosen set. Mutual visibility and  its variants have been studied for a number of classical graph families—such as 
paths, cycles, cographs, grids, and various product graphs—and all four  visibility parameters are NP-complete to compute in general.

In this talk, we also focus on visibility parameters in three different graph  families: Kneser graphs, bipartite Kneser graphs, and Johnson graphs. The obtained results for the total mutual-visibility number of Kneser and bipartite Kneser  graphs are related to the size of transversal-critical uniform hypergraphs, while for Johnson graphs we show that the total mutual-visibility number equals a  corresponding hypergraph Turán number. We further establish exact values or  estimations for the mutual-visibility number over these graph classes, revealing  new connections between visibility constraints and external properties of  uniform hypergraphs.