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
Saad I. El-Zanati
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.

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  • Communicated by Adam Paweł Wojda.
  • Received: 2019-08-28.
  • Revised: 2020-01-23.
  • Accepted: 2020-01-23.
  • Published online: 2020-03-09.
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Cite this article as:
Ryan C. Bunge, Dontez Collins, Daryl Conko-Camel, Saad I. El-Zanati, Rachel Liebrecht, Alexander Vasquez, Maximum packings of the λ-fold complete 3-uniform hypergraph with loose 3-cycles, Opuscula Math. 40, no. 2 (2020), 209-225, https://doi.org/10.7494/OpMath.2020.40.2.209

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