Dirac's theorem
E1335241
UNEXPLORED
Dirac's theorem is a fundamental result in graph theory that gives a simple degree condition on the vertices of a finite graph guaranteeing the existence of a Hamiltonian cycle.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Dirac's theorem canonical | 1 |
| Dirac’s theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T18628478 — 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: Dirac's theorem Context triple: [Hamiltonian cycle, sufficientCondition, Dirac's theorem]
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A.
Gallai theorem
Gallai's theorem is a fundamental result in graph theory and Ramsey theory that characterizes the structure of colorings of complete graphs by guaranteeing large monochromatic or well-organized subgraphs.
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B.
Erdős–Gallai theorem
The Erdős–Gallai theorem is a fundamental result in graph theory that characterizes which sequences of nonnegative integers can occur as the degree sequences of simple graphs.
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C.
Turán's theorem
Turán's theorem is a fundamental result in extremal graph theory that determines the maximum number of edges a graph can have without containing a complete subgraph of a given size.
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D.
König's theorem in graph theory
König's theorem in graph theory is a fundamental result in bipartite graphs stating that the size of a maximum matching equals the size of a minimum vertex cover.
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E.
Menger theorem in graph theory
Menger's theorem in graph theory is a fundamental result that characterizes the connectivity between two vertices in a graph by equating the maximum number of pairwise internally disjoint paths between them with the minimum size of a vertex cut separating them.
- 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: Dirac's theorem Target entity description: Dirac's theorem is a fundamental result in graph theory that gives a simple degree condition on the vertices of a finite graph guaranteeing the existence of a Hamiltonian cycle.
-
A.
Gallai theorem
Gallai's theorem is a fundamental result in graph theory and Ramsey theory that characterizes the structure of colorings of complete graphs by guaranteeing large monochromatic or well-organized subgraphs.
-
B.
Erdős–Gallai theorem
The Erdős–Gallai theorem is a fundamental result in graph theory that characterizes which sequences of nonnegative integers can occur as the degree sequences of simple graphs.
-
C.
Turán's theorem
Turán's theorem is a fundamental result in extremal graph theory that determines the maximum number of edges a graph can have without containing a complete subgraph of a given size.
-
D.
König's theorem in graph theory
König's theorem in graph theory is a fundamental result in bipartite graphs stating that the size of a maximum matching equals the size of a minimum vertex cover.
-
E.
Menger theorem in graph theory
Menger's theorem in graph theory is a fundamental result that characterizes the connectivity between two vertices in a graph by equating the maximum number of pairwise internally disjoint paths between them with the minimum size of a vertex cut separating them.
- F. None of above. chosen
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Hamiltonian cycle concept
subject linked to:
Pósa’s theorem in graph theory
linked to: Dirac's theorem