Theorem

Baranyai's Theorem

Combinatorics and Graph Theory

Baranyai's Theorem states that whenever k divides n, the collection of all k-element subsets of an n-element set can be partitioned into perfect matchings, meaning it can be split into groups each of which itself partitions the full n-element set into disjoint k-element blocks. Named for Zsolt Baranyai, it is a foundational existence result of design theory and hypergraph combinatorics, resolving the natural generalization of round-robin tournament scheduling from ordinary graphs to uniform hypergraphs.

Facts

Statement

Whenever k divides n, the k-element subsets of an n-element set can be partitioned into perfect matchings, each one itself a partition of the full n-element set into disjoint k-element blocks. 1

Proof Year

1975 1

Classification

Statement Form

Existence Theorem 1

Connections

Has Statement Form

Existence Theorem

In Branch

Combinatorics

Source Baranyai's theorem (Wikipedia)

Proved By

Zsolt Baranyai

Source Baranyai's theorem (Wikipedia)

Sources

1. Baranyai's theorem (Wikipedia)

Wikimedia Foundation

History section
The general case was proved by Zsolt Baranyai in 1975.
Proved By: Zsolt Baranyai, Lead
The general case was proved by Zsolt Baranyai in 1975.
In Branch: Combinatorics, Lead paragraph
In combinatorial mathematics, Baranyai's theorem (proved by and named after Zsolt Baranyai) deals with the decompositions of complete hypergraphs.
In Group: Enumerative, Additive and Algebraic Combinatorics, Lead section
In combinatorial mathematics, Baranyai's theorem (proved by and named after

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Baranyai's Theorem

Has Statement Form

In Branch

Proved By