Seven Bridges of Königsberg problem
E105766
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Seven Bridges of Königsberg problem canonical | 2 |
| Königsberg bridges problem | 1 |
| Seven Bridges of Koenigsberg problem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T890978 — 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: Seven Bridges of Königsberg problem Context triple: [Königsberg, famousFor, Seven Bridges of Königsberg problem]
-
A.
Königsberg
Königsberg was a historic Prussian city on the Baltic Sea, renowned as a major cultural and intellectual center of East Prussia and later known as Kaliningrad.
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B.
Mathematical Bridge
The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
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C.
Entscheidungsproblem
The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
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D.
Marco Polo Bridge
Marco Polo Bridge is a historic stone bridge near Beijing, China, renowned both for its distinctive carved stone lions and as the site of the 1937 clash that marked the start of full-scale war between China and Japan.
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E.
Magere Brug
Magere Brug is a historic and picturesque white wooden drawbridge in Amsterdam, renowned as one of the city's most iconic canal crossings.
- 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: Seven Bridges of Königsberg problem Target entity description: 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.
-
A.
Königsberg
Königsberg was a historic Prussian city on the Baltic Sea, renowned as a major cultural and intellectual center of East Prussia and later known as Kaliningrad.
-
B.
Mathematical Bridge
The Mathematical Bridge is a famous wooden footbridge at Queens' College, Cambridge, known for its elegant arch that is constructed entirely from straight timbers.
-
C.
Entscheidungsproblem
The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
-
D.
Marco Polo Bridge
Marco Polo Bridge is a historic stone bridge near Beijing, China, renowned both for its distinctive carved stone lions and as the site of the 1937 clash that marked the start of full-scale war between China and Japan.
-
E.
Magere Brug
Magere Brug is a historic and picturesque white wooden drawbridge in Amsterdam, renowned as one of the city's most iconic canal crossings.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
graph theory problem
ⓘ
historical puzzle ⓘ mathematical problem ⓘ topology problem ⓘ |
| alsoKnownAs |
Seven Bridges of Königsberg problem
ⓘ
surface form:
Königsberg bridges problem
Seven Bridges of Königsberg problem ⓘ
surface form:
Seven Bridges of Koenigsberg problem
|
| answer | no such walk exists ⓘ |
| asksQuestion | whether there exists a walk crossing each bridge exactly once ⓘ |
| conclusion | no Eulerian trail exists for the Königsberg bridge graph ⓘ |
| condition |
each bridge must be crossed exactly once
ⓘ
start and end points may be anywhere ⓘ |
| field |
discrete mathematics
ⓘ
graph theory ⓘ recreational mathematics ⓘ topology ⓘ |
| hasConcept |
Eulerian circuit
ⓘ
Eulerian trail ⓘ
surface form:
Eulerian path
Eulerian trail ⓘ connected graph ⓘ degree of a vertex ⓘ graph abstraction ⓘ parity of vertex degrees ⓘ |
| hasOriginLocation |
Königsberg
ⓘ
Prussia ⓘ present-day Kaliningrad ⓘ |
| historicalSignificance |
early problem in graph theory
ⓘ
foundational problem in topology ⓘ |
| inspired |
applications of graph theory to real-world routing problems
ⓘ
study of networks ⓘ |
| involves |
Pregel River
ⓘ
land masses ⓘ seven bridges ⓘ |
| keyResult |
Königsberg bridge graph has four vertices of odd degree
ⓘ
a connected graph has an Eulerian trail iff it has exactly zero or two vertices of odd degree ⓘ |
| ledTo |
development of graph theory
ⓘ
development of topology ⓘ |
| modernCityName |
Königsberg
ⓘ
surface form:
Kaliningrad
|
| originalCityName | Königsberg ⓘ |
| publicationYear | 1736 ⓘ |
| publishedIn | “Solutio problematis ad geometriam situs pertinentis” ⓘ |
| publishedInLanguage | Latin ⓘ |
| relatedTo |
Eulerian graph
ⓘ
Hamiltonian cycle concept ⓘ
surface form:
Hamiltonian path problem
geometria situs ⓘ graph traversal ⓘ |
| solutionMethod |
modeling land masses as vertices and bridges as edges
ⓘ
using degrees of vertices to determine existence of Eulerian path ⓘ |
| solvedBy | Leonhard Euler ⓘ |
| timePeriod | 18th century ⓘ |
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: Seven Bridges of Königsberg problem Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Königsberg bridges problem
this entity surface form:
Seven Bridges of Koenigsberg problem