Szekeres snark
E386032
The Szekeres snark is a famous cubic graph in graph theory that serves as a counterexample in edge-coloring problems and helped advance the study of snark graphs.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Szekeres snark canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3757269 — 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: Szekeres snark Context triple: [George Szekeres, notableWork, Szekeres snark]
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A.
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.
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B.
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.
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C.
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.
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D.
Tucker’s lemma
Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
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E.
Sperner's lemma
Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
- 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: Szekeres snark Target entity description: The Szekeres snark is a famous cubic graph in graph theory that serves as a counterexample in edge-coloring problems and helped advance the study of snark graphs.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
Tucker’s lemma
Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
-
E.
Sperner's lemma
Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
- F. None of above. chosen
Statements (29)
| Predicate | Object |
|---|---|
| instanceOf |
bridgeless cubic graph
ⓘ
cubic graph ⓘ non-3-edge-colorable graph ⓘ snark graph ⓘ |
| chromaticIndex | 4 ⓘ |
| chromaticNumber | 3 ⓘ |
| contributedTo | development of snark theory ⓘ |
| edgeChromaticIndex | 4 ⓘ |
| field | graph theory ⓘ |
| girth | 5 ⓘ |
| hasEdgeConnectivity | 3 ⓘ |
| hasProperty |
bridgeless
ⓘ
connected graph ⓘ cubic ⓘ cyclically 4-edge-connected ⓘ non-Hamiltonian ⓘ non-planar ⓘ regular of degree 3 ⓘ simple graph ⓘ snark ⓘ triangle-free ⓘ |
| isComparedWith |
Blanuša snarks
ⓘ
Flower snark ⓘ Petersen graph ⓘ |
| isCounterexampleTo | 3-edge-colorability of bridgeless cubic graphs ⓘ |
| isUsedAs |
counterexample in edge-coloring problems
ⓘ
example in the study of snark graphs ⓘ |
| namedAfter | George Szekeres ⓘ |
| vertexDegree | 3 ⓘ |
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: Szekeres snark Description of subject: The Szekeres snark is a famous cubic graph in graph theory that serves as a counterexample in edge-coloring problems and helped advance the study of snark graphs.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.