Hamiltonian cycle concept

E455347

cycle in a graph decision problem graph theory concept

The Hamiltonian cycle concept is a fundamental idea in graph theory describing a cycle that visits each vertex of a graph exactly once and returns to the starting point.

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All labels observed (6)

Label	Occurrences
HAMILTONIAN CYCLE	1
Hamiltonian Cycle problem	1
Hamiltonian cycle concept canonical	1
Hamiltonian cycle problem	1
Hamiltonian graphs	1
Hamiltonian path problem	1

How this entity was disambiguated

This entity first appeared as the object of triple T4585391 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Hamiltonian cycle concept
Context triple: [William Rowan Hamilton, knownFor, Hamiltonian cycle concept]

A. Seven Bridges of Königsberg problem
The Seven Bridges of Königsberg problem is a historic puzzle in graph theory that asks whether one can walk through the city of Königsberg crossing each of its seven bridges exactly once, leading Euler to found the field of topology.
B. Conway's 99-graph problem
Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
C. Conway's thrackle conjecture
Conway's thrackle conjecture is an unsolved problem in combinatorial geometry asserting that in any drawing of a graph where every pair of edges meets exactly once, the number of edges cannot exceed the number of vertices.
D. Conway circle theorem
The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
E. de Bruijn sequence
A de Bruijn sequence is a cyclic sequence over a given alphabet in which every possible subsequence of a fixed length appears exactly once.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Hamiltonian cycle concept
Target entity description: The Hamiltonian cycle concept is a fundamental idea in graph theory describing a cycle that visits each vertex of a graph exactly once and returns to the starting point.

A. Seven Bridges of Königsberg problem
The Seven Bridges of Königsberg problem is a historic puzzle in graph theory that asks whether one can walk through the city of Königsberg crossing each of its seven bridges exactly once, leading Euler to found the field of topology.
B. Conway's 99-graph problem
Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
C. Conway's thrackle conjecture
Conway's thrackle conjecture is an unsolved problem in combinatorial geometry asserting that in any drawing of a graph where every pair of edges meets exactly once, the number of edges cannot exceed the number of vertices.
D. Conway circle theorem
The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
E. de Bruijn sequence
A de Bruijn sequence is a cyclic sequence over a given alphabet in which every possible subsequence of a fixed length appears exactly once.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	cycle in a graph ⓘ decision problem ⓘ graph theory concept ⓘ
alsoCalled	Hamiltonian circuit ⓘ Hamiltonian tour ⓘ
appearsIn	network design ⓘ polyhedral combinatorics ⓘ routing problems ⓘ
appliesTo	directed graphs ⓘ undirected graphs ⓘ
asks	whether a given graph contains a Hamiltonian cycle ⓘ
complexityClass	NP-complete ⓘ
complexityOfRecognition	NP-complete in general graphs ⓘ
contrastedWith	Eulerian cycle ⓘ linked to: Eulerian trail
decisionProblem	Hamiltonian cycle problem ⓘ
definition	a cycle in a graph that visits each vertex exactly once and returns to the starting vertex ⓘ
edgeConstraint	uses only edges of the graph ⓘ
exampleGraphWith	complete graph Kn for n ≥ 3 ⓘ
exampleGraphWithout	star graph Kn,1 for n ≥ 2 ⓘ tree with more than two vertices ⓘ
existsIn	Hamiltonian graph ⓘ
field	graph theory ⓘ
generalizedTo	infinite graphs with appropriate definitions ⓘ
historicalOrigin	Icosian game of William Rowan Hamilton ⓘ
isSubgraphOf	underlying graph ⓘ
length	number of vertices in the graph ⓘ
namedAfter	William Rowan Hamilton ⓘ
property	spans all vertices of the graph ⓘ
relatedConcept	Eulerian cycle ⓘ Hamiltonian path ⓘ
representation	sequence of vertices forming a simple cycle ⓘ
requires	finite graph in standard definition ⓘ graph to be connected for existence ⓘ
returnsTo	starting vertex ⓘ
specialCaseOf	cycle ⓘ
studiedIn	algorithmic graph theory ⓘ extremal graph theory ⓘ
sufficientCondition	Bondy–Chvátal theorem ⓘ Chvátal–Erdős theorem ⓘ linked to: Bondy–Chvátal theorem Dirac's theorem ⓘ Ore's theorem ⓘ
tractableOn	graphs of bounded treewidth ⓘ tournaments ⓘ
usedIn	combinatorial optimization ⓘ computational complexity theory ⓘ linked to: Complexity Theory traveling salesman problem ⓘ
vertexConstraint	includes every vertex of the graph ⓘ
visitsEachVertex	exactly once ⓘ

How these facts were elicited