Ore's theorem

E1335242 UNEXPLORED

Ore's theorem is a fundamental result in graph theory that gives a degree-based criterion guaranteeing a simple graph contains a Hamiltonian cycle.

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All labels observed (3)

Label	Occurrences
Ore's theorem canonical	2
Ore's theorem in graph theory	1
Ore’s theorem	1

How this entity was disambiguated

This entity first appeared as the object of triple T18628479 — 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: Ore's theorem
Context triple: [Hamiltonian cycle, sufficientCondition, Ore's theorem]

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. 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.
C. 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.
D. 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.
E. Erdős–Stone theorem
The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
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: Ore's theorem
Target entity description: Ore's theorem is a fundamental result in graph theory that gives a degree-based criterion guaranteeing a simple graph contains 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. 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.
C. 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.
D. 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.
E. Erdős–Stone theorem
The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
F. None of above. chosen