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A connected 1-factorisation is a 1-factorisation of a hypergraph for whichthe union of each pair of distinct 1-factors is a connected hypergraph. Auniform 1-factorisation is a 1-factorisation of a hypergraph for which theunion of each pair of distinct 1-factors is isomorphic to the samesubhypergraph, and a uniform-connected 1-factorisation is a uniform1-factorisation in which that subhypergraph is connected. Chen and Lu [Journalof Algebraic Combinatorics, 46(2) 475--497, 2017] describe a family of1-factorisations of the complete 3-uniform hypergraph on $q+1$ vertices, where$q\equiv 2\pmod 3$ is a prime power. In this paper, we show that theirconstruction yields a connected 1-factorisation only when $q=2,5,11$ or $q=2^p$for some odd prime $p$, and a uniform 1-factorisation only for $q=2,5,8$ (eachof these is a uniform-connected 1-factorisation).

An Infinite Family of Connected 1-Factorisations of Complete 3-Uniform Hypergraphs