bibkey: bozovic2026limiteddomination authors: D. Božović year: 2026 title: “On k-limited domination: complexity and Sierpiński graphs” doi: 10.48550/arXiv.2610.01584 url: https://arxiv.org/abs/2610.01584v1 claim: “Conjecture 12 (§6): Let n, m, and k be integers such that n ≥ 1 and 1 ≤ k ≤ m − 1. Then γ_k^L(S(n, m)) = (m − k)·m^(n−1).” strata_touched:

• D5/S3/Combinatorics/Graph/SierpinskiLimitedDomination license: citation-only triage: anchor

Božović, On k-limited domination: complexity and Sierpiński graphs

D. Božović’s arXiv:2610.01584v1 studies limited domination in Sierpiński graphs. Section 6, Conjecture 12 (p. 9) states verbatim:

Let n, m, and k be integers such that n ≥ 1 and 1 ≤ k ≤ m − 1. Then γ_k^L(S(n, m)) = (m − k)·m^(n−1).

The graph and parameter definitions used by the formal statement are given in Section 2. The exact formula is proved here by a recursive coloring constant on linking edges and a lower-bound charging argument over the base cliques. The source’s Theorems 10 and 11 are the special cases k = 1 and m = 3.

Verified locator

• DOI: https://doi.org/10.48550/arXiv.2610.01584
• URL: https://arxiv.org/abs/2610.01584v1
• Locator: §2 for the definitions of S(n,m), k-limited domination, and γ_k^L; §6, Conjecture 12 for the quoted formula.