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.
Facts
Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source Grinberg's theorem (Wikipedia)
Principal Result Of
Source Emanuels Grīnbergs (Wikipedia)
Proved By
Source Grinberg's theorem (Wikipedia)
Sources
1. Grinberg's theorem (Wikipedia)
Lead paragraph
who proved it in 1968
Proved By: Emanuel Grinberg, Lead sentence
Grinberg's theorem is named after Latvian mathematician Emanuel Grinberg, 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
View the SourceEmanuels Grīnbergs (Wikipedia)
Principal Result Of: Emanuel Grinberg, LeadQuote, Principal Result Of: Emanuel Grinberg, Lead
known for Grinberg's theorem on the Hamiltonicity of planar graphs
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.