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Maximum packings of the a-fold complete 3-uniform hypergraph with loose 3-cycles

Bunge Ryan C., Collins Dontez, Conko-Camel Daryl, El-Zanati Saad I., Liebrecht Rachel, Vasquez Alexander

Opuscula Mathematica

2020

Vol. 40, no. 2

209--225

It is known that the 3-uniform loose 3-cycle decomposes the complete 3-uniform hypergraph of order v if and only if v ≡0, 1, or 2 (mod 9). For all positive integers λand v, we find a maximum packing with loose 3-cycles of the λ-fold complete 3-uniform hypergraph of order v. We show that, if v ≥6, such a packing has a leave of two or fewer edges.