如果 
, 那麼在 
-均勻 超圖 在 
個頂點上分解為 1-因子，其中 1-因子是一組 
個兩兩不相交的 
-集。 Brouwer 和 Schrijver (1979) 給出了一個優美的證明，使用了 最大流最小割定理 的 網路流。
巴拉尼定理
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參考文獻
Baranyai, Z. "On the Factorization of the Complete Uniform Hypergraph. Infinite and Finite Sets." In Infinite and Finite Sets, Vol. 1. Proceedings of a Colloquium held at Keszthely, June 25-July 1, 1973. Dedicated to Paul Erdős on his 60th Birthday (Ed. A. Hajnal, R. Rado, and V. T. Sós). Amsterdam, Netherlands: North-Holland, pp. 91-108, 1975.Brouwer, A. E. and Schrijver, A. "Uniform Hypergraphs." In Packing and Covering in Combinatorics. Mathematical Centre Tracts, No. 106, pp. 39-73, 1979.Tamm, U. "Applications of Baranyai's Theorem in Information Theory." In Proceedings of 6th Benelux-Japan Workshop on Coding and Information Theory, Essen, 1996 (Ed. A. J. Han Vinck and A. van Wijngaarden). Shannon Foundation, 1996. http://www.mathematik.uni-bielefeld.de/ahlswede/pub/tamm/baranyai.ps.van Lint, J. H. and Wilson, R. M. A Course in Combinatorics. New York: Cambridge University Press, pp. 476-479, 1993.West, D. "Re: disjoint cliques, resolutions of designs?" GRAPHNET@listserv.nodak.edu posting. Feb. 25, 2004. http://listserv.nodak.edu/scripts/wa.exe?A2=ind0402&L=graphnet&F=&S=&P=4041.在 中被引用
巴拉尼定理請引用為
韋斯坦因，埃裡克·W. “巴拉尼定理。” 來自 —— 資源。 https://mathworld.tw/BaranyaisTheorem.html