On 2-Factorizations of the Complete 3-Uniform Hypergraph of Order 12 Minus a 1-Factor

A k-factorization of the complete t-uniform hypergraph \(K^{(t)}_{v}\) is an H-decomposition of \(K^{(t)}_{v}\) where H is a k-regular spanning subhypergraph of \(K^{(t)}_{v}\) . It is known that seven of the eight non-isomorphic 3-uniform 2-regular hypergraphs of order \(v\le 9\) factorize \(K^{(3)}_v\) . We use nauty to generate the 2-regular spanning subhypergraphs of \(K^{(3)}_{12}\) and show that they all factorize \(K^{(3)}_{12}-I\) , where I is a 1-factor.