Seven Bridges of Königsberg problem

E105766

graph theory problem historical puzzle mathematical problem topology problem

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.

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All labels observed (5)

Label	Occurrences
Seven Bridges of Königsberg	3
Seven Bridges of Königsberg problem canonical	2
Königsberg bridges	1
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.
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
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	Königsberg bridges problem ⓘ linked to: Seven Bridges of Königsberg problem Seven Bridges of Koenigsberg problem ⓘ linked to: Seven Bridges of Königsberg 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 path ⓘ linked to: Eulerian trail 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	Kaliningrad ⓘ linked to: Königsberg
originalCityName	Königsberg ⓘ
publicationYear	1736 ⓘ
publishedIn	“Solutio problematis ad geometriam situs pertinentis” ⓘ
publishedInLanguage	Latin ⓘ
relatedTo	Eulerian graph ⓘ Hamiltonian path problem ⓘ linked to: Hamiltonian cycle concept 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