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DECOMPOSING COMPLETE 3-UNIFORM HYPERGRAPH Kn³ INTO 7-CYCLES.
- Source :
- Opuscula Mathematica; 2019, Vol. 39 Issue 3, p383-393, 11p
- Publication Year :
- 2019
-
Abstract
- We use the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph. A decomposition of complete fc-uniform hypergraph K<subscript>n</subscript><superscript>k</superscript>into Hamiltonian cycles was studied by Bailey-Stevens and Meszka-Rosa. For n = 2,4, 5 (mod 6), we design an algorithm for decomposing the complete 3-uniform hypergraphs into Hamiltonian cycles by using the method of edge-partition. A decomposition of K<subscript>n</subscript>³ into 5-cycles has been presented for all admissible n ≤ 17, and for all n = 4m + 1 when m is a positive integer. In general, the existence of a decomposition into 5-cycles remains open. In this paper, we show if 42 Ι (n - 1)(n- 2) and if there exist λ = (n-1)(n-2)/42 sequences (k<subscript>i0</subscript>,k<subscript>i1</subscript>,...,k<subscript>i6</subscript>) on D<subscript>all</subscript>(n), then K<subscript>n</subscript>(³) can be decomposed into 7-cycles. We use the method of edge-partition and cycle sequence. We find a decomposition of K<subscript>37</subscript>(³) and K<subscript>43</subscript>(³ ) into 7-cycles. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 12329274
- Volume :
- 39
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Opuscula Mathematica
- Publication Type :
- Academic Journal
- Accession number :
- 134931866
- Full Text :
- https://doi.org/10.7494/OpMath.2019.39.3.383