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

• Autorzy: Lakshmi R , Poovaragavan T.

Identyfikatory

DOI

10.7494/OpMath.2020.40.4.509

• Języki publikacji: EN

Abstrakty

EN

A complete 3-unilorm hypergraph of order n has vertex set V with \V\ = n and the set ol all 3-subsets of V as its edge set. A t-cycle in this hypergraph is v1, e1, v2, e2,… , vt, et, v1 where v1, v2,…vt are distinct vertices and e1, e-2,..., et are distinct edges such that [formula] and [formula] 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-unilorm hypergraph of order n into p-cycles, whenever p is prime.

Słowa kluczowe

EN

uniform hypergraph; cycle decomposition

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2020
• Tom: Vol. 40, no. 4
• Strony: 509--516
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Lakshmi R

• Annamalai University Department of Mathematics Annamalainagar-608 002, India
• Dharumapuram Gnanambigai Government Arts College for Women Department of Mathematics Mayiladuthurai-609 001, India

autor

Poovaragavan T.

• Annamalai University Department of Mathematics Annamalainagar-608 002, India

Bibliografia

• [1] C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam, 1979.
• [2] J.C. Bermond, Hamiltonian decompositions of graphs, directed graphs and hypergraphs, Ann. Discrete Math. 3 (1978), 21-28.
• [3] J.C. Bermond, A. Germa, M.C. Heydemann, D. Sotteau, Hypergraphes hamiltoniens, [in:] Problemes combinatoires et theorie des graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976), Colloq. Internat. CNRS, vol. 260, CNRS, Paris, 1978, 39-43.
• [4] D. Bryant, S. Herke, B. Maenhaut, W. Wannasit, Decompositions of complete i-uniform hypergraphs into small 3-uniform hypergraphs, Australas. J. Combin. 60 (2014) 2, 227-254.
• [5] H. Jordon, G. Newkirk, A-cycle decompositions of complete 3-uniform, hypergraphs, Australas. J. Combin. 71 (2018) 2, 312-323.
• [6] D. Kiihn, D. Osthus, Decompositions of complete uniform hypergraphs into Hamilton Berge cycles, J. Combin. Theory Ser. A 126 (2014), 128-135.
• [7] R. Lakshmi, T. Poovaragavan, 6-Cycle decompositions of complete 3-uniform hypergraphs, (submitted).
• [8] P. Petecki, On cyclic hamiltonian decompositions of complete k-uniform hypergraphs, Discrete Math. 325 (2014), 74-76.
• [9] M. Truszczyński, Note on the decomposition of \Km>n (Aif^.n) into paths, Discrete Math. 55 (1985), 89-96.
• [10] H. Verrall, Hamilton decompositions of complete Z-uniform hypergraphs, Discrete Math. 132 (1994), 333-348.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).