| Title: | k-Domination ivariants on Kneser graphs |
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| Authors: | ID Brešar, Boštjan (Author)
ID Dravec, Tanja (Author)
ID Cornet, María Gracia (Author)
ID Henning, Michael A. (Author) |
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| Files: |  AMC_Bresar,Dravec,Cornet,Henning_2025.pdf (375,34 KB)
MD5: 380698D5811748CA25E94683B67A7B07
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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: | In this follow-up to work of M.G. Cornet and P. Torres from 2023, where the k-tuple domination number and the 2-packing number in Kneser graphs K(n, r) were studied, we are concerned with two variations, the k-domination number, γ_k(K(n, r)), and the k-tuple total domination number,
γ_{t × k}(K(n, r)), of K(n, r). For both invariants we prove monotonicity results by showing that γ_k(K(n, r)) ≥ γ_k(K(n + 1, r)) holds for any n ≥ 2(k + r), and γ_{t × k}(K(n, r)) ≥
γ_{t × k}(K(n + 1, r)) holds for any n ≥ 2r + 1. We prove that γ_k(K(n, r)) = γ_{t × k}(K(n, r)) = k + r when n ≥ r(k + r), and that in this case every γ_(k)-set and γ_(t × k)-set is a clique, while γ_k(r(k + r) − 1, r) = γ_{t × k}(r(k + r) − 1, r) = k + r + 1, for any k ≥ 2. Concerning the 2-packing number, ρ₂(K(n, r)), of K(n, r), we prove the exact values of ρ₂(K(3r − 3, r)) when r ≥ 10, and give sufficient conditions for ρ₂(K(n, r)) to be equal to some small values by imposing bounds on r with respect to n. We also prove a version of monotonicity for the 2-packing number of Kneser graphs. |
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| Keywords: | Kneser graphs, k-domination, k-tuple total domination, 2-packing |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 24.07.2025 |
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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. 4, [article no.] P4.02 |
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| PID: | 20.500.12556/RUP-22016  |
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| UDC: | 519.17 |
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| eISSN: | 1855-3974 |
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| DOI: | https://doi.org/10.26493/1855-3974.3294.7fd |
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| Publication date in RUP: | 22.10.2025 |
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| Views: | 251 |
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| Downloads: | 1 |
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