Theorem

Grinberg's Theorem

Combinatorics and Graph Theory

Grinberg's theorem, in graph theory, gives a necessary condition, based on the lengths of the faces of a planar embedding, for a planar graph to have a Hamiltonian cycle; a graph that fails the condition cannot be Hamiltonian. Established in 1968 by the Latvian mathematician Emanuel Grinberg, the theorem follows readily from Euler's formula and has been used to construct counterexamples to Tait's conjecture about Hamiltonian cycles in cubic polyhedral graphs. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts

Classification

Statement Form

Characterization Theorem 1

Proof Year

1968 1

Connections

Has Statement Form

Characterization

In Branch

Graph Theory

Source Grinberg's theorem (Wikipedia)

Sources

1. Grinberg's theorem (Wikipedia)

Lead paragraph
who proved it in 1968
In Branch: Graph Theory, Lead sentence
In graph theory, Grinberg's theorem is a necessary condition for a planar graph to contain a Hamiltonian cycle, based on the lengt
In Group: Graph Theory, Lead section
In graph theory, Grinberg's theorem is a necessary condition

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Grinberg's Theorem

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In Branch