Cornet–Dravec–Torres conjecture for domination in odd Johnson graphs J(n, 3)

Let $J(n,3)$ be the Johnson graph with vertex set $\binom{[n]}{3}$, where two $3$-subsets are adjacent if and only if they share exactly two elements. Let $\gamma(J(n,3))$ denote its domination number, and let $\phi_n$ be the residue-class quantity defined from the Fort–Hedlund covering numbers.

Cornet–Dravec–Torres conjecture. For every odd integer $n\ge 7$,

$$\gamma(J(n,3))=\phi_n.$$

Cornet, Dravec, and Torres conjectured this formula after determining the corresponding value for every even $n\ge 6$. The present paper proves the odd case, so the conjecture is solved; together with the even case, this determines the domination number of $J(n,3)$ for every $n\ge 6$.