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arxiv: 2606.10326 · v1 · pith:I737USD3new · submitted 2026-06-09 · 🧮 math.CO

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

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

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