Domination in Johnson graphs J(n, 3) for odd n

Abstract

In 2025 Cornet, Dravec, and Torres determined the domination number $γ(J(n, 3))$ of the Johnson graph for every even $n \ge 6$, expressing it as a closed form $ϕ_n$ in terms of Fort\textendash{}Hedlund covering numbers, and conjectured the same value for odd $n$. We prove this conjecture: $γ(J(n, 3)) = ϕ_n$ for every odd $n \ge 7$, completing the determination of $γ(J(n, 3))$ for all $n \ge 6$.