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.

Rights

URN

URN:NBN:SI:doc-L2G170UO

COBISSID

270605059

DOI

10.26493/1855-3974.3344.4c8

Added

27.10.2026

Metadata

Citation

APA:

Boruzanli Ekinci, Gülnaz, Bujtás, Csilla (2025). Mutual-visibility problems in Kneser and Johnson graphs. Ars mathematica contemporanea, volume 25, issue 3, article p3.07, str. 1-16. URN:NBN:SI:doc-L2G170UO from http://www.dlib.si

MLA:

Boruzanli Ekinci, Gülnaz, Bujtás, Csilla. "Mutual-visibility problems in Kneser and Johnson graphs." Ars mathematica contemporanea volume 25. issue 3. article p3.07 (2025) str. 1-16.
<http://www.dlib.si/?URN=URN:NBN:SI:doc-L2G170UO>