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gptkbp:instance_of
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gptkb:theorem
|
|
gptkbp:applies_to
|
graph theory
network flow problems
circuit design
|
|
gptkbp:criteria
|
planarity of graphs
graph planarity
|
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gptkbp:has_expansion
|
other types of graphs
|
|
gptkbp:has_impact_on
|
network design
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Kuratowski's theorem
|
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gptkbp:is_a_basis_for
|
graph drawing algorithms
|
|
gptkbp:is_a_framework_for
|
the study of planar graphs
graph theory research
|
|
gptkbp:is_analyzed_in
|
graph structures
|
|
gptkbp:is_associated_with
|
subdivision of graphs
|
|
gptkbp:is_connected_to
|
gptkb:Euler's_formula
|
|
gptkbp:is_described_as
|
characterization of planar graphs
|
|
gptkbp:is_discussed_in
|
graph theory textbooks
|
|
gptkbp:is_essential_for
|
gptkb:technology
|
|
gptkbp:is_fundamental_to
|
graph drawing
|
|
gptkbp:is_often_associated_with
|
academic papers
|
|
gptkbp:is_often_used_in
|
gptkb:computer_science
|
|
gptkbp:is_part_of
|
graph theory curriculum
|
|
gptkbp:is_related_to
|
topological graph theory
planarity testing
|
|
gptkbp:is_tested_for
|
the four color theorem
|
|
gptkbp:is_used_in
|
gptkb:television_channel
algorithm design
|
|
gptkbp:is_utilized_in
|
geographic information systems
|
|
gptkbp:key
|
graph theory
graph algorithms
|
|
gptkbp:legal_issue
|
provides a method for testing planarity
|
|
gptkbp:named_after
|
gptkb:Kazimierz_Kuratowski
|
|
gptkbp:occurs_in
|
gptkb:Mathematician
|
|
gptkbp:published_by
|
gptkb:1930
|
|
gptkbp:resulted_in
|
combinatorial topology
Kazimierz Kuratowski's work
|
|
gptkbp:significance
|
graph theory
the study of planar embeddings
|
|
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
|
|
gptkbp:subject
|
mathematical research
mathematical proofs
|
|
gptkbp:training
|
discrete mathematics courses
|
|
gptkbp:bfsParent
|
gptkb:Kazimierz_Kuratowski
gptkb:Steinhaus–_Borsuk–_Lebesgue–_Kuratowski–_Zorn_theorem
|
|
gptkbp:bfsLayer
|
6
|