Conway's 99-graph problem
E266110
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Conway's 99-graph problem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2426178 — 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: Conway's 99-graph problem Context triple: [John H. Conway, hasConcept, Conway's 99-graph problem]
-
A.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
-
B.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
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C.
Conway–Norton collaboration
The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
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D.
A Combinatorial Problem
"A Combinatorial Problem" is a classic mathematical paper by N. G. de Bruijn that introduces and analyzes a fundamental counting problem in combinatorics.
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E.
Hilbert’s twenty-third problem
Hilbert’s twenty-third problem is one of David Hilbert’s famous list of unsolved problems, focusing on the further development and systematic application of the calculus of variations.
- 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: Conway's 99-graph problem Target entity description: 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.
-
A.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
-
B.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
-
C.
Conway–Norton collaboration
The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
-
D.
A Combinatorial Problem
"A Combinatorial Problem" is a classic mathematical paper by N. G. de Bruijn that introduces and analyzes a fundamental counting problem in combinatorics.
-
E.
Hilbert’s twenty-third problem
Hilbert’s twenty-third problem is one of David Hilbert’s famous list of unsolved problems, focusing on the further development and systematic application of the calculus of variations.
- F. None of above. chosen
Statements (26)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial problem
ⓘ
open problem in graph theory ⓘ |
| appearsIn | research on unsolved problems in graph theory ⓘ |
| concerns | existence of a 99-vertex graph with specific adjacency constraints ⓘ |
| describes | hypothetical graph with highly constrained adjacency conditions ⓘ |
| difficulty | hard ⓘ |
| field | graph theory ⓘ |
| hasProperty |
concerns a single finite simple graph
ⓘ
global existence question ⓘ involves strong local adjacency constraints ⓘ |
| hasUnknown |
structure of the 99-vertex graph if it exists
ⓘ
whether such a 99-vertex graph exists ⓘ |
| namedAfter | John H. Conway ⓘ |
| namedEntityType | mathematical problem ⓘ |
| openAsOf | 2024 ⓘ |
| posedBy | John H. Conway ⓘ |
| relatedTo |
Ramsey theory
ⓘ
finite combinatorics ⓘ graph coloring problems ⓘ |
| status | unsolved ⓘ |
| studiedIn |
combinatorics
ⓘ
discrete mathematics ⓘ |
| topic |
extremal graph theory
ⓘ
graph adjacency properties ⓘ regular graphs ⓘ |
| vertexCount | 99 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Conway's 99-graph problem Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
John H. Conway