On maximum packings of λ-fold complete 3-uniform hypergraphs with triple-hyperstars of size 4

Amber Armstrong, Ryan C. Bunge, William Duncan, Saad I. El-Zanati, Kristin Koe, Rachel Stutzman


A symmetric triple-hyperstar is a connected, 3-uniform hypergraph where, for some edge {a, b, c}, vertices a, b, and c all have degree k > 1 and all other edges contain exactly 2 vertices of degree 1. Let H denote the symmetric triple-hyperstar with 4 edges and, for positive integers λ and v, let λKv(3) denote the λ-fold complete 3-uniform hypergraph on v vertices. We find maximum packings of λKv(3) with copies of H.


hypergraph decomposition; maximum packing; hypergraph design

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DOI: http://dx.doi.org/10.5614/ejgta.2021.9.2.17


P. Adams, D. Bryant, and M. Buchanan, A survey on the existence of G-designs, J. Combin. Des. 16 (2008), 373–410.

R.F. Bailey and B. Stevens, Hamiltonian decompositions of complete k-uniform hypergraphs, Discrete Math. 310 (2010), 3088–3095.

Zs. Baranyai, On the factorization of the complete uniform hypergraph, in: Infinite and finite sets, Colloq. Math. Soc. Janos Bolyai 10, North-Holland, Amsterdam, 1975, 91–108.

J.C. Bermond, A. Germa and D. Sotteau, Hypergraph-designs, Ars Combinatoria 3 (1977), 47–66.

D. Bryant, S. Herke, B. Maenhaut, and W. Wannasit, Decompositions of complete 3-uniform hypergraphs into small 3-uniform hypergraphs, Australas. J. Combin. 60 (2014), 227–254.

D.E. Bryant and T.A. McCourt, Existence results for G-designs, http://wiki.smp.uq.edu.au/G-designs/

R.C. Bunge, S.I. El-Zanati, L. Haman, C. Hatzer, K. Koe and K. Spornberger, On loose 4-cycle decompositions of complete 3-uniform hypergraphs, submitted.

C.J. Colbourn and J.H. Dinitz (Editors), Handbook of Combinatorial Designs, 2nd ed., Chapman & Hall/CRC Press, Boca Raton, FL, 2007.

C.J. Colbourn and R.Mathon, “Steiner systems,” in [8], pp. 102–110.

S. Glock, D. Kuhn, A. Lo and D. Osthus, The existence of designs via iterative absorption, arXiv:1611.06827v2, (2017), 63 pages.

S. Glock, D. Kuhn, A. Lo and D. Osthus, Hypergraph F-designs for arbitrary F, arXiv:1706.01800, (2017), 72 pages.

H. Hanani, On quadruple systems, Canad. J. Math., 12 (1960), 145-57.

H. Hanani, Decomposition of hypergraphs into octahedra, Second International Conference on Combinatorial Mathematics (New York, 1978), pp. 260–264, Ann. New York Acad. Sci., 319, New York Acad. Sci., New York, 1979.

H. Jordon and G. Newkirk, 4-cycle decompositions of complete 3-uniform hypergraphs, Australas. J. Combin. 71 (2018), 312–323.

P. Keevash, The existence of designs, arXiv:1401.3665v2, (2018), 39 pages.

G.B. Khosrovshahi and R. Laue, “t-designs with t ≥ 3,” in [8], pp. 79-101.

J. Kuhl and M.W. Schroeder, Hamilton cycle decompositions of k-uniform k-partite hypergraphs, Australas. J. Combin. 56 (2013), 23-37.

D. Kuhn and D. Osthus, Decompositions of complete uniform hypergraphs into Hamilton Berge cycles, J. Combin. Theory Ser. A 126 (2014), 128–135.

Z. Lonc, Solution of a delta-system decomposition problem, J. Combin. Theory, Ser. A 55 (1990), 33–48.

Z. Lonc, Packing, covering and decomposing of a complete uniform hypergraph into deltasystems, Graphs Combin. 8 (1992), 333–341.

M. Meszka and A. Rosa, Decomposing complete 3-uniform hypergraphs into Hamiltonian cycles, Australas. J. Combin. 45 (2009), 291–302.

A.F. Mouyart and F. Sterboul, Decomposition of the complete hypergraph into delta-systems II, J. Combin. Theory, Ser. A 41 (1986), 139–149.

M.W. Schroeder, On Hamilton cycle decompositions of r-uniform r-partite hypergraphs, Discrete Math. 315 (2014), 1–8.

R.M. Wilson, Decompositions of Complete Graphs into Subgraphs Isomorphic to a Given Graph, in “Proc. Fifth British Combinatorial Conference” (C. St. J. A. Nash-Williams and J. Sheehan, Eds.), pp. 647–659, Congr. Numer. XV, 1975.


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