Mutual-visibility problems in Kneser and Johnson graphsBoruzanli Ekinci, Gülnaz (Avtor) Bujtás, Csilla (Avtor) mutual-visibility settotal mutual-visibility setKneser graphbipartite Kneser graphJohnson graphTurán-type problemcovering designLet $G$ be a connected graph and $X \subseteq V(G)$. By definition, two vertices $u$ and $v$ are $X$-visible in $G$ if there exists a shortest $u, v$-path with all internal vertices being outside of the set $X$. The largest size of $X$ such that any two vertices of $G$ (resp. any two vertices from $X$) are $X$-visible is the total mutual-visibility number (resp. the mutual-visibility number) of ▫$G$▫. In this paper, we determine the total mutual-visibility number of Kneser graphs, bipartite Kneser graphs, and Johnson graphs. The formulas proved for Kneser, and bipartite Kneser graphs are related to the size of transversal-critical uniform hypergraphs, while the total mutual-visibility number of Johnson graphs is equal to a hypergraph Turán number. Exact values or estimates for the mutual-visibility number over these graph classes are also established.20252026-03-05 13:05:52Članek v reviji180300UDK: 519.17ISSN pri članku: 1855-3966DOI: 10.26493/1855-3974.3344.4c8COBISS_ID: 270605059sl