| Title: | Mutual-visibility problems in Kneser and Johnson graphs |
|---|
| Authors: | ID Boruzanli Ekinci, Gülnaz (Author)
ID Bujtás, Csilla (Author) |
|---|
| Files: |  PDF - Presentation file, download (427,55 KB)
MD5: 528E7AEC3E608DBA2122D7B978E56F92
 URL - Source URL, visit https://amc-journal.eu/index.php/amc/article/view/3344
|
|---|
| Language: | English |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
|
|---|
| Abstract: | 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. |
|---|
| Keywords: | mutual-visibility set, total mutual-visibility set, Kneser graph, bipartite Kneser graph, Johnson graph, Turán-type problem, covering design |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 01.01.2025 |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | 16 str. |
|---|
| Numbering: | Vol. 25, no. 3, article no. P3.07 |
|---|
| PID: | 20.500.12556/DiRROS-27987  |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 1855-3966 |
|---|
| DOI: | 10.26493/1855-3974.3344.4c8 |
|---|
| COBISS.SI-ID: | 270605059 |
|---|
| Note: |
|
|---|
| Publication date in DiRROS: | 05.03.2026 |
|---|
| Views: | 1709 |
|---|
| Downloads: | 246 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
