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.
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StatementEvery cubic, bridgeless graph contains a perfect matching. 1 Classification
Statement Form Petersen's Theorem
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Source Petersen's theorem (Wikipedia)
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1. Petersen's theorem (Wikipedia)
Introduction
Every cubic, bridgeless graph contains a perfect matching.
Article text
The theorem appears first in the 1891 article "Die Theorie der regulären graphs".
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:
In Group: Graph Theory, Lead section
In the mathematical discipline of graph theory, Petersen's theorem, named after Julius Petersen
View the SourceJulius Petersen (Wikipedia)
Principal Result Of: Julius Petersen, Article textQuote, Principal Result Of: Julius Petersen, Article text
(iv) The factorization of regular graphs of odd degree, in particular, the theorem that any bridgeless 3-regular graph can be decomposed into a l-factor and a 2-factor (Petersen's theorem).
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