See also Kneser Graph
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References 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 Brouwer, A. E. and Schrijver, A. "Uniform
Hypergraphs." In Packing
and Covering in Combinatorics. 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. 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 . Referenced
on Wolfram|Alpha Baranyai's Theorem
Cite this as:
Weisstein, Eric W. "Baranyai's Theorem."
From MathWorld https://mathworld.wolfram.com/BaranyaisTheorem.html
Subject classifications
,
then the complete 
-uniform
hypergraph on 
vertices decomposes into 1-factors, where a 1-factor is a
set of 
pairwise disjoint 
-sets.
Brouwer and Schrijver (1979) give a beautiful proof using the maximum
flow, minimum cut theorem of network flows.
