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.

Full text (pdf)

• R. Lakshmi (corresponding author)
• 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.
• Accepted: 2020-06-05.
• Published online: 2020-07-09.