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Barnette's conjecture

Barnette's conjecture is an unsolved problem in graph theory, a branch of mathematics, concerning Hamiltonian cycles in graphs. It is named after David W. Barnette, a professor emeritus at the University of California, Davis; it states that every bipartite polyhedral graph with three edges per vertex has a Hamiltonian cycle.

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Definitions

Planar graphUndirected graphEmbeddedEuclidean planeCrossings
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History

P. G.Tait1969Tait's conjectureW. T.TutteCounterexample
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Equivalent forms

Induced subgraphs
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Partial results

NP-complete
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Barnette's conjecture

Nodes35
Edges34
Triples101
Avg. degree1.94
Density0.057143
Components1

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Barnette's conjecture

Top relations

related to References · 72
Barnette's conjecture → Academic Press, Akiyama, Alexander, American Mathematical Society Translations, Australasian Journal, Barnette's, Barnette-Goodey Conjecture, Bau, BF02757273, Brendan, Carlos, Combinatorial Theory, Combinatorics, Conjecture, Constructions, David, Discrete Mathematics, ECCC TR06-015Florek, Hamiltonian, Helmut
related to Partial results · 9
Barnette's conjecture → Alt, Although, Another, Barnette's, Hamiltonian, Hamiltonicity, If, If Barnette's, NP-complete
related to Definitions · 8
Barnette's conjecture → And, Barnette's, By Steinitz's, Euclidean, Finally, Hamiltonian, Then, Therefore
related to Equivalent forms · 7
Barnette's conjecture → Barnette, Barnette's, Clearly, Hamiltonian, In, Kelmans, The
related to External links · 5
Barnette's conjecture → Eric, MathWorldBarnette's Conjecture, Open Problem Garden, Robert Samal, Weisstein

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Important terminology

hamiltonian bipartite graph cubic conjecture barnette's every polyhedral mr doi graphs mathematics cycle vertices polyhedron 10 edges counterexample planar journal

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Barnette's conjecturerelated to DefinitionsEuclidean0.60section
Barnette's conjecturerelated to DefinitionsFinally0.60section
Barnette's conjecturerelated to DefinitionsHamiltonian0.60section
Barnette's conjecturerelated to DefinitionsBarnette's0.60section
Barnette's conjecturerelated to DefinitionsBy Steinitz's0.60section
Barnette's conjecturerelated to DefinitionsAnd0.60section
Barnette's conjecturerelated to DefinitionsTherefore0.60section
Barnette's conjecturerelated to DefinitionsThen0.60section
Barnette's conjecturerelated to Equivalent formsKelmans0.60section
Barnette's conjecturerelated to Equivalent formsBarnette's0.60section
Barnette's conjecturerelated to Equivalent formsHamiltonian0.60section
Barnette's conjecturerelated to Equivalent formsClearly0.60section

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