Leírás
Consider a connected graph $G$ and a set $X \subseteq V(G)$. We say that two vertices $u$ and $v$ are $X$-visible 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 from $X$ are $X$-visible is the mutual-visibility number of $G$. If the visibility is required for every two vertices from $V(G)$, the largest cardinality is the total mutual-visibility number.
In the talk, we first survey some results on these visibility invariants to point out connections to well-known combinatorial problems. In the main part, we concentrate on 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.
(joint work with Gülnaz Boruzanli Ekinci)
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https://us06web.zoom.us/j/2572885125?omn=84501050120