Fary's Theorem is a result of graph theory stating that every simple planar graph can be drawn in the plane without any crossing edges using only straight line segments, so that permitting curved edges gives no advantage over straight ones for the class of graphs drawable without crossings. Named for Istvan Fary, it was proved independently by Fary, Klaus Wagner, and Sherman K. Stein.
Facts
StatementEvery simple planar graph can be drawn in the plane with no crossing edges using only straight line segments. 1 Classification
Statement Form 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 Fary's theorem (Wikipedia)
Proved By
Source Fary's theorem (Wikipedia)
Sources
1. Fary's theorem (Wikipedia)
Lead section
any simple, planar graph can be drawn without crossings so that its edges are straight line segments.
- In Branch: Graph Theory, Lead sentence
Proved By: Klaus Wagner, Lead paragraph
to be drawn. The theorem is named after István Fáry, although it was proved independently by Klaus Wagner (1936), Fáry (1948), and Sherman K. Stein (1951).
View the Source2. Fáry's theorem (Wikipedia)
Wikipedia Fáry's theorem lead paragraph (w-bbfill-psymath4-0926)Quote, Wikipedia Fáry's theorem lead paragraph (w-bbfill-psymath4-0926)
proved independently by Klaus Wagner (1936
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