Top

Published in:

2024 | OriginalPaper | Chapter

Decomposing the \(\lambda \)-Fold Complete 3-Uniform Hypergraph into the Lines of the Pasch Configuration

Authors : Ryan C. Bunge, Skyler R. Dodson, Saad I. El-Zanati, Jacob Franzmeier, Dru Horne

Published in: Combinatorics, Graph Theory and Computing

Publisher: Springer Nature Switzerland

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Let P denote the 3-uniform hypergraph on 6 vertices whose edges form the lines of the Pasch configuration. We give necessary and sufficient conditions for the existence of P-decompositions of the \(\lambda \)-fold complete 3-uniform hypergraph on v vertices.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Properties of Sierpinski Triangle Graphs

next chapter On Decompositions of the Johnson Graph

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

M. Akin, R. C. Bunge, S. I. El-Zanati, J. Hamilton, B. Kolle, S. Lehmann, and L. Neiburger, On tight 6-cycle decompositions of complete 3-uniform hypergraphs, Discrete Math.345 (2022), 112676. M. Akin, R. C. Bunge, S. I. El-Zanati, J. Hamilton, B. Kolle, S. Lehmann, and L. Neiburger, On tight 6-cycle decompositions of complete 3-uniform hypergraphs, Discrete Math., to appear.

Zs. Baranyai, On the factorization of the complete uniform hypergraph, in: Infinite and finite sets, Colloq. Math. Soc. János Bolyai10, North-Holland, Amsterdam, 1975, 91–108.

J.-C. Bermond, A. Germa, and D. Sotteau,Hypergraph-designs, Ars Combinatoria3 (1977), 47–66.MathSciNet

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.MathSciNet

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

R. C. Bunge, D. Collins, D. Conko-Camel, S. I. El-Zanati, R. Liebrecht, and A. Vasquez, Maximum packings of the \(\lambda \)-fold complete 3-uniform hypergraph with loose 3-cycles, Opuscula Math.40 (2020), 209–225.MathSciNetCrossRef

R. C. Bunge, B. D. Darrow, S. I. El-Zanati, K. P. Hadaway, M. K. Pryor, A. J. Romer, A. Squires, and A. C. Stover, On tight 9-cycle decompositions of complete 3-uniform hypergraphs, Australas. J. Combin.80 (2021), 233–240.MathSciNet

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, Bull. Inst. Combin. Appl.87 (2019), 75–84.MathSciNet

10.

R. C. Bunge, S. I. El-Zanati, J. Jeffries, and C. Vanden Eynden, Edge orbits and cyclic and r-pyramidal decompositions of complete uniform hypergraphs, Discrete Math.341 (2018), 3348–3354.MathSciNetCrossRef

11.

R. C. Bunge, S. I. El-Zanati, J. Jetton, M. Juarez, A. J. Netz, D. Roberts, and P. Ward, On loose 5-cycle decompositions, packings, and coverings of complete \(\lambda \)-fold 3-uniform hypergraphs, Ars Combin., to appear.

12.

C. J. Colbourn and R. Mathon, Steiner systems, in The CRC Handbook of Combinatorial Designs, 2nd edition, (Eds. C. J. Colbourn and J. H. Dinitz), CRC Press, Boca Raton (2007), 102–110.

13.

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

14.

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

15.

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

16.

G. B. Khosrovshahi and R. Laue, t-designs with \(t\geq 3\), in The CRC Handbook of Combinatorial Designs, 2nd edition, (Eds. C. J. Colbourn and J. H. Dinitz), CRC Press, Boca Raton (2007), 79–101.

17.

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.

Title: Decomposing the -Fold Complete 3-Uniform Hypergraph into the Lines of the Pasch Configuration
Authors: Ryan C. Bunge
Skyler R. Dodson
Saad I. El-Zanati
Jacob Franzmeier
Dru Horne
Publisher: Springer Nature Switzerland
Book: Combinatorics, Graph Theory and Computing
Print ISBN: 978-3-031-62165-9

Electronic ISBN: 978-3-031-62166-6

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-62166-6_22

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"