A note on the linear cycle cover conjecture of Gyárfás and Sárközy (Q1753119)

Summary: A linear cycle in a \(3\)-uniform hypergraph \(H\) is a cyclic sequence of hyperedges such that any two consecutive hyperedges intersect in exactly one element and non-consecutive hyperedges are disjoint. Let \(\alpha(H)\) denote the size of a largest independent set of \(H\). We show that the vertex set of every \(3\)-uniform hypergraph \(H\) can be covered by at most \(\alpha(H)\) edge-disjoint linear cycles (where we accept a vertex and a hyperedge as a linear cycle), proving a weaker version of a conjecture of \textit{A. Gyárfás} and \textit{G. Sárközy} [Electron. J. Comb. 21, No. 2, Research Paper P2.36, 10 p. (2014; Zbl 1300.05199)].