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Theorem

Hajnal-Szemeredi Theorem

Combinatorics and Graph Theory

The Hajnal-Szemeredi theorem, in graph theory, states that any graph with maximum degree Delta has an equitable coloring using Delta plus 1 colors, meaning a proper coloring whose color classes are as close to equal in size as possible. Paul Erdos conjectured the result in 1964, and Andras Hajnal and Endre Szemeredi proved it in 1970; polynomial-time algorithms exist for finding such a coloring within this bound. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Classification
Statement Form
Existence Theorem 1
Proof Year
1970 1
Connections

Has Statement Form

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Source Equitable coloring (Wikipedia)

Proved By

Source Equitable coloring (Wikipedia)
Sources
1. Equitable coloring (Wikipedia)
  • Lead paragraph
    proven by András Hajnal and Endre Szemerédi (1970)
  • In Branch: Graph Theory, Lead sentence
    In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph,
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