Steinhaus chessboard theorem
E394470
The Steinhaus chessboard theorem is a combinatorial result in geometry and topology that gives conditions under which certain colored paths must exist on a checkerboard-like grid.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Steinhaus chessboard theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3884669 — 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: Steinhaus chessboard theorem Context triple: [Hugo Steinhaus, notableWork, Steinhaus chessboard theorem]
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A.
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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B.
Erdős–Szekeres theorem
The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
-
C.
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.
-
D.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
E.
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.
- 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: Steinhaus chessboard theorem Target entity description: The Steinhaus chessboard theorem is a combinatorial result in geometry and topology that gives conditions under which certain colored paths must exist on a checkerboard-like grid.
-
A.
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.
-
B.
Erdős–Szekeres theorem
The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
-
C.
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.
-
D.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
E.
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.
- F. None of above. chosen
Statements (35)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial theorem
ⓘ
mathematical theorem ⓘ result in geometric topology ⓘ |
| appearsIn |
expository texts on Hugo Steinhaus’s problems
ⓘ
literature on geometric combinatorics ⓘ |
| concerns |
combinatorial properties of planar subdivisions
ⓘ
connectivity properties of colored squares ⓘ paths joining opposite sides of a rectangle or square ⓘ |
| context |
checkerboard colorings
ⓘ
grid graphs ⓘ planar cell decompositions ⓘ |
| field |
combinatorics
ⓘ
geometry ⓘ topology ⓘ |
| hasAspect |
discrete analogue of continuum topological results
ⓘ
parity and connectivity arguments ⓘ |
| hasGeneralization |
results on colored paths in higher-dimensional grids
ⓘ
variants for more than two colors ⓘ |
| hasProofMethod |
combinatorial topology
ⓘ
parity arguments on adjacency graphs ⓘ |
| implies | existence of a path of one color between two opposite sides under suitable boundary conditions ⓘ |
| namedAfter | Hugo Steinhaus ⓘ |
| relatedTo |
Borsuk–Ulam theorem
ⓘ
linked to:
Tucker’s lemma
Jordan curve theorem ⓘ discrete geometry ⓘ topological combinatorics ⓘ |
| subject |
colored paths on a checkerboard-like grid
ⓘ
conditions forcing connecting paths between opposite sides of a board ⓘ existence of monochromatic paths ⓘ |
| typeOfResult | existence theorem ⓘ |
| usedIn |
combinatorial proofs in topology
ⓘ
mathematical olympiad style problems ⓘ problems about unavoidable paths in grids ⓘ |
| uses |
finite grids
ⓘ
two-colorings of squares ⓘ |
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: Steinhaus chessboard theorem Description of subject: The Steinhaus chessboard theorem is a combinatorial result in geometry and topology that gives conditions under which certain colored paths must exist on a checkerboard-like grid.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.