| Naslov: | k-Domination ivariants on Kneser graphs |
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| Avtorji: | ID Brešar, Boštjan (Avtor)
ID Dravec, Tanja (Avtor)
ID Cornet, María Gracia (Avtor)
ID Henning, Michael A. (Avtor) |
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| Datoteke: |  AMC_Bresar,Dravec,Cornet,Henning_2025.pdf (375,34 KB)
MD5: 380698D5811748CA25E94683B67A7B07
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Članek v reviji |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | ZUP - Založba Univerze na Primorskem
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| Opis: | 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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| Ključne besede: | Kneser graphs, k-domination, k-tuple total domination, 2-packing |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 24.07.2025 |
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| Založnik: | Založba Univerze na Primorskem |
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| Leto izida: | 2025 |
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| Št. strani: | 16 str. |
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| Številčenje: | Vol. 25, no. 4, [article no.] P4.02 |
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| PID: | 20.500.12556/RUP-22016  |
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| UDK: | 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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| Datum objave v RUP: | 22.10.2025 |
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| Število ogledov: | 187 |
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| Število prenosov: | 1 |
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| Metapodatki: |    |
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