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gptkbp:instance_of
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gptkb:theorem
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gptkbp:applies_to
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graph theory
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gptkbp:can_be_used_to_prove
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the four color theorem
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gptkbp:criteria
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planarity of graphs
graph planarity
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gptkbp:describes
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characterization of planar graphs
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gptkbp:has_expansion
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other types of graphs
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gptkbp:has_implications_for
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network design
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https://www.w3.org/2000/01/rdf-schema#label
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Kuratowski's theorem
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gptkbp:is_a_basis_for
|
graph drawing algorithms
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gptkbp:is_a_foundation_for
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the study of planar graphs
graph theory research
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gptkbp:is_a_subject_of
|
mathematical research
mathematical proofs
|
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gptkbp:is_a_theorem_in
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gptkb:Mathematics
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gptkbp:is_analyzed_in
|
graph structures
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gptkbp:is_applicable_to
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network flow problems
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gptkbp:is_associated_with
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subdivision of graphs
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gptkbp:is_connected_to
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gptkb:Euler's_formula
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gptkbp:is_discussed_in
|
graph theory textbooks
|
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gptkbp:is_essential_for
|
gptkb:Graphics_Processing_Unit
|
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gptkbp:is_fundamental_to
|
graph drawing
|
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gptkbp:is_often_referenced_in
|
academic papers
|
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gptkbp:is_often_used_in
|
gptkb:computer_science
|
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gptkbp:is_part_of
|
graph theory curriculum
|
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gptkbp:is_related_to
|
topological graph theory
planarity testing
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gptkbp:is_relevant_to
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circuit design
|
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gptkbp:is_significant_for
|
graph theory
the study of planar embeddings
|
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gptkbp:is_taught_in
|
discrete mathematics courses
|
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gptkbp:is_used_in
|
gptkb:topology
algorithm design
|
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gptkbp:is_utilized_in
|
geographic information systems
|
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gptkbp:key
|
graph theory
|
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gptkbp:key_concept
|
graph algorithms
|
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gptkbp:legal_principle
|
provides a method for testing planarity
|
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gptkbp:named_after
|
gptkb:Kazimierz_Kuratowski
|
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gptkbp:published_by
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gptkb:1930
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gptkbp:state
|
a graph is planar if and only if it does not contain a subgraph that is a subdivision of K5 or K3,3
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gptkbp:was_a_result_of
|
combinatorial topology
Kazimierz Kuratowski's work
|
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gptkbp:bfsParent
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gptkb:Kazimierz_Kuratowski
gptkb:Steinhaus–_Borsuk–_Lebesgue–_Kuratowski–_Zorn_theorem
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gptkbp:bfsLayer
|
7
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