Theorem

Petersen's Theorem

Combinatorics and Graph Theory

Petersen's Theorem states that every bridgeless graph in which each vertex has exactly three edges, called a cubic graph, has a perfect matching, meaning a set of edges pairing up all its vertices with none left out and none shared between two pairs. Named for Julius Petersen, it was one of the earliest results of graph theory and was later strengthened to show that every such graph in fact decomposes into a perfect matching together with a collection of disjoint cycles covering the remaining edges.

Facts

Classification

Statement Form

Existence Theorem 1

Statement

Every cubic, bridgeless graph contains a perfect matching. 1

Connections

Has Statement Form

Existence Theorem

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

Graph Theory

Source Petersen's theorem (Wikipedia)

Proved By

Julius Petersen

Source Petersen's theorem (Wikipedia)

Sources

1. Petersen's theorem (Wikipedia)

Introduction
Every cubic, bridgeless graph contains a perfect matching.
In Branch: Graph Theory, Lead sentence
In the mathematical discipline of graph theory, Petersen's theorem, named after Julius Petersen, is one of the earliest results in
Proved By: Julius Petersen, Lead paragraph
In the mathematical discipline of graph theory, Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated as follows:

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Petersen's Theorem

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Proved By