20.500.12556/RUL-180300 Mutual-visibility problems in Kneser and Johnson graphs Let $G$ 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. mutual-visibility set total mutual-visibility set Kneser graph bipartite Kneser graph Johnson graph Turán-type problem covering design množica vzajemne vidnosti množica celotne vzajemne vidnosti Kneserjev graf dvodelni Kneserjev graf Johnsonov graf problem Turánovega tipa pokrivni načrt true false true Angleški jezik Slovenski jezik Članek v reviji 2026-03-05 13:05:52 2026-03-05 13:05:57 2026-03-06 04:33:08 0000-00-00 00:00:00 2025 0 0 16 str. no. 3, article no. P3.07 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-01-01 519.17 1855-3966 10.26493/1855-3974.3344.4c8 270605059 amc_3344.pdf amc_3344.pdf 1 D14816B3358086FC4A142E10A796B879 f22f8b839453aa164dd082f50500d3fc703c7ec07c6b285bd10309f19fce5cd9 f7c98870-188b-11f1-a1ba-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=229524 https://amc-journal.eu/index.php/amc/article/view/3344 1 4bf2f7be-188b-11f1-a1ba-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=229523 Fakulteta za matematiko in fiziko 0 0 0