20.500.12556/RUP-22016 k-Domination ivariants on Kneser graphs k-dominacijske invariante Kneserjevih grafov 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. Kneser graphs k-domination k-tuple total domination 2-packing Kneserjevi grafi k-dominacija k-terna popolna dominacija 2-pakiranje true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-10-22 21:27:48 2025-10-22 21:27:48 2025-11-14 03:06:28 0000-00-00 00:00:00 2025 0 0 16 str. no. 4, [article no.] P4.02 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-07-24 519.17 1855-3974 https://doi.org/10.26493/1855-3974.3294.7fd AMC_Bresar,Dravec,Cornet,Henning_2025.pdf AMC_Bresar,Dravec,Cornet,Henning_2025.pdf 1 380698D5811748CA25E94683B67A7B07 3a70ea42f542a80d887d25fab9b2d1f2a215410e736c1082f0701d3935b56c2f c0cbc4a8-af7f-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31951 Založba Univerze na Primorskem 0 0 0