Theorem

Tutte Homotopy Theorem

Combinatorics and Graph Theory

Tutte's homotopy theorem, introduced by W. T. Tutte in 1958, extends the graph-theoretic notion of a path to matroids, showing that any closed path in a matroid can be written as a composition of elementary closed paths, so that in a precise sense every closed path is homotopic to the trivial closed path. The result generalizes an intuition from graph theory, that a cycle can be broken down into simpler cycles, into the more abstract setting of matroid theory, where the underlying structure need not come from a graph at all.

Facts

Statement

In a matroid, any closed path can be written as a composition of elementary closed paths, so that in a precise sense every closed path is homotopic to the trivial closed path. 1

Proof Year

1958 1

Classification

Statement Form

Existence Theorem 1

Connections

Has Statement Form

Existence Theorem

In Branch

Combinatorics

Source Tutte homotopy theorem (Wikipedia)

Proved By

W. T. Tutte

Source Tutte homotopy theorem (Wikipedia)

Sources

1. Tutte's homotopy theorem, Wikipedia

Lede section, opening clause
Tutte's homotopy theorem, introduced by Tutte (1958)
Lede section, closing clause
generalises the concept of "path" from graphs to matroids, and states roughly that closed paths can be written as compositions of elementary closed paths, so that in some sense they are homotopic to the trivial closed path.

View the Source

Tutte homotopy theorem (Wikipedia)

In Branch: Combinatorics, Lead
generalises the concept of "path" from graphs to matroids
In Group: Graph Theory, Lead
In mathematics, Tutte's homotopy theorem, introduced by Tutte (1958), generalises the concept of "path" from graphs to matroids, and states roughly that closed paths can be written as compositions of elementary closed paths, so that in some sense they are homotopic to the trivial closed path.
Proved By: W. T. Tutte, Lead paragraph
In mathematics, Tutte's homotopy theorem, introduced by Tutte (1958), generalises the concept of "path" from graphs to matroids, and states roughly

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Tutte Homotopy Theorem

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Proved By