Among all graphs on a fixed number of vertices that contain no complete subgraph of a given size, the maximum possible number of edges is achieved uniquely by a specific balanced complete multipartite graph, the Turan graph. Proved by Pal Turan, it founded extremal graph theory.
Facts
StatementTuran's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given size. 1 Classification
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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
Proved By
Source Turan's Theorem (Wikipedia)
Sources
1. Turan's Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, opening sentence
Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given size.
lead paragraph, sentence naming the year first described
Turán's theorem, and the Turán graphs giving its extreme case, were first described and studied by Hungarian mathematician Pál Turán in 1941.
Proved By: Pal Turan, Lead paragraph
In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph
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