| Title: | Mutual-visibility problems in Kneser and Johnson graphs |
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| Authors: | ID Boruzanlı Ekinci, Gülnaz (Author)
ID Bujtás, Csilla (Author) |
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| Files: |  AMC_Boruzanlı_Ekinci,Bujtas_2025.pdf (426,16 KB)
MD5: D14816B3358086FC4A142E10A796B879
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | Let G be a connected graph and X ⊆ 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 estimations for the mutual-visibility number over these graph classes are also established. |
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| Keywords: | mutual-visibility set, total mutual-visibility set, Kneser graph, bipartite Kneser graph, Johnson graph, Turán-type problem, covering design |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 06.06.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 16 str. |
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| Numbering: | Vol. 25, no. 3, [article no.] P3.07 |
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| PID: | 20.500.12556/RUP-22011  |
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| UDC: | 519.17 |
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| eISSN: | 1855-3974 |
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| DOI: | https://doi.org/10.26493/1855-3974.3344.4c8 |
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| Publication date in RUP: | 22.10.2025 |
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| Views: | 309 |
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| Downloads: | 6 |
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