Opuscula Math. 40, no. 4 (2020), 509-516
https://doi.org/10.7494/OpMath.2020.40.4.509

 
Opuscula Mathematica

Decompositions of complete 3-uniform hypergraphs into cycles of constant prime length

R. Lakshmi
T. Poovaragavan

Abstract. A complete \(3\)-uniform hypergraph of order \(n\) has vertex set \(V\) with \(|V|=n\) and the set of all \(3\)-subsets of \(V\) as its edge set. A \(t\)-cycle in this hypergraph is \(v_1, e_1, v_2, e_2,\dots, v_t, e_t, v_1\) where \(v_1, v_2,\dots, v_t\) are distinct vertices and \(e_1, e_2,\dots, e_t\) are distinct edges such that \(v_i, v_{i+1}\in e_i\) for \(i \in \{1, 2,\dots, t-1\}\) and \(v_t, v_1 \in e_t\). A decomposition of a hypergraph is a partition of its edge set into edge-disjoint subsets. In this paper, we give necessary and sufficient conditions for a decomposition of the complete \(3\)-uniform hypergraph of order \(n\) into \(p\)-cycles, whenever \(p\) is prime.

Keywords: uniform hypergraph, cycle decomposition.

Mathematics Subject Classification: 05C65, 05C85.

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  • R. Lakshmi (corresponding author)
  • ORCID iD https://orcid.org/0000-0001-9633-7676
  • Annamalai University, Department of Mathematics, Annamalainagar-608 002, India
  • Dharumapuram Gnanambigai Government Arts College for Women, Department of Mathematics, Mayiladuthurai-609 001, India
  • Communicated by Andrzej Żak.
  • Received: 2020-01-12.
  • Accepted: 2020-06-05.
  • Published online: 2020-07-09.
Opuscula Mathematica - cover

Cite this article as:
R. Lakshmi, T. Poovaragavan, Decompositions of complete 3-uniform hypergraphs into cycles of constant prime length, Opuscula Math. 40, no. 4 (2020), 509-516, https://doi.org/10.7494/OpMath.2020.40.4.509

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