Opuscula Math. 40, no. 2 (2020), 209-225
https://doi.org/10.7494/OpMath.2020.40.2.209

Opuscula Mathematica

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

Ryan C. Bunge
Dontez Collins
Daryl Conko-Camel
Rachel Liebrecht
Alexander Vasquez

Abstract. It is known that the 3-uniform loose 3-cycle decomposes the complete 3-uniform hypergraph of order $$v$$ if and only if $$v \equiv 0, 1,\text{ or }2\ (\operatorname{mod} 9)$$. For all positive integers $$\lambda$$ and $$v$$, we find a maximum packing with loose 3-cycles of the $$\lambda$$-fold complete 3-uniform hypergraph of order $$v$$. We show that, if $$v \geq 6$$, such a packing has a leave of two or fewer edges.

Keywords: maximum packing, $$\lambda$$-fold complete 3-uniform hypergraph, loose 3-cycle.

Mathematics Subject Classification: 05C65, 05C85.

Full text (pdf)

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• Communicated by Adam Paweł Wojda.
• Revised: 2020-01-23.
• Accepted: 2020-01-23.
• Published online: 2020-03-09.