In graph theory, the planarity testing problem is the algorithmic problem of testing whether a given graph is a planar graph (that is, whether it can be drawn in the plane without edge intersections). This is a well-studied problem in computer science for which many practical algorithms have emerged, many taking advantage of novel data structures. Most…
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Planarity testing topic overview
The analysis highlights Science, Planarity criteria and Algorithms as prominent areas in the source structure around Planarity testing.
Related topics
52
Source areas
3
Connected nodes
55
Extracted relationships
59
Concept neighborhoods
26
Bridge connections
55
What this topic covers Research coverage
Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.
Algorithms · 24 topics
Planarity criteria · 20 topics
Overview · 8 topics
Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.
Key facts & relationships
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Explore all related topics Closing gaps
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.
Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
How Planarity testing connects Entity context
Entity context groups extracted connections by relationship type. Counts show recurrence in the analyzed source; the examples are research signals, not claims about importance.
The extracted context around Planarity testing shows recurring relationship patterns in the source. For example, Planarity testing → Algorithms, Boyer, Fraysseix, Furthermore, In, John Boyer, K3, K5, Kuratowski, Mendez, Myrvold, Ossona, Otherwise, PQ, Rosenstiehl, See, The, This, Wendy Myrvold, Williamson Another extracted example is Planarity testing → Ackermann, Demaine, Di Battista, Dynamic Algorithms, Eppstein, Galil, Holm, In, Italiano, La Poutré, Planarity, Pătrașcu, Rotenberg, Sarnak, Spencer, Tamassia, Westbrook. Use these groups to spot repeated connection types before inspecting the individual relationships.
Planarity testing
Top relations
related to Edge addition method· 20
Planarity testing → Algorithms, Boyer, Fraysseix, Furthermore, In, John Boyer, K3, K5, Kuratowski, Mendez, Myrvold, Ossona, Otherwise, PQ, Rosenstiehl, See, The, This, Wendy Myrvold, Williamson
related to Dynamic algorithms· 17
Planarity testing → Ackermann, Demaine, Di Battista, Dynamic Algorithms, Eppstein, Galil, Holm, In, Italiano, La Poutré, Planarity, Pătrașcu, Rotenberg, Sarnak, Spencer, Tamassia, Westbrook
related to Path addition method· 13
Planarity testing → Algorithms, An, Efficient Data, Hopcroft, In, Library, Mehlhorn, Mutzel, Näher, Tarjan, Tarjan's, Taylor, The
Relationships are represented as Subject → Predicate → Object triples. Confidence describes extraction strength, not the real-world importance of a relationship; lower-confidence rows may be contextual rather than explicit.
TTTA extracted 59 structured relationships around Planarity testing. Examples in this analysis include a Kuratowski subgraph if it is not → instance of → or an obstacle to planarity and Planarity testing → related to Dynamic algorithms → Planarity. The table shows each extracted connection, where it came from and its confidence.
Subject
Predicate
Object
Confidence
Src
a Kuratowski subgraph if it is not
instance of
or an obstacle to planarity
0.80
text
Planarity testing
related to Dynamic algorithms
Planarity
0.60
section
Planarity testing
related to Dynamic algorithms
Dynamic Algorithms
0.60
section
Planarity testing
related to Dynamic algorithms
In
0.60
section
Planarity testing
related to Dynamic algorithms
Ackermann
0.60
section
Planarity testing
related to Dynamic algorithms
La Poutré
0.60
section
Planarity testing
related to Dynamic algorithms
Di Battista
0.60
section
Planarity testing
related to Dynamic algorithms
Tamassia
0.60
section
Planarity testing
related to Dynamic algorithms
Westbrook
0.60
section
Planarity testing
related to Dynamic algorithms
Pătrașcu
0.60
section
Planarity testing
related to Dynamic algorithms
Demaine
0.60
section
Planarity testing
related to Dynamic algorithms
Holm
0.60
section
No triples extracted yet.
Related concept clusters Concept neighborhoods
Concept neighborhoods group terms that sit near one another in the extracted graph. They are useful for discovering adjacent language and context, but proximity does not by itself imply a factual relationship.
The concept neighborhoods around Planarity testing bring nearby vocabulary together. In this analysis, examples include Testing, Planar and Algorithms. Use the clusters to find adjacent concepts and terminology that may deserve separate research.
Planarity testing
Testing
Planar
Algorithms
Criterion
Fraysseix
Rosenstiehl
Theory
Algorithm
Test
Graphs
One
Path
planarity testing
Testing
Algorithms
Theory
Planar
Algorithm
Criterion
Fraysseix
Rosenstiehl
Test
Graphs
One
Path
graph theory
Planar
Edge
Testing
Graphs
Planarity
Subgraph
Given
Graph
Theorem
Theory
Algorithms
Criterion
algorithms
Algorithm
Testing
Planarity
Graph
Criterion
Fraysseix
One
Problem
Rosenstiehl
Theory
Data
Edges
planar graph
Planar
Graphs
Embedding
Testing
Planarity
Subgraph
Method
Criterion
Theorem
Theory
Algorithm
Given
graph embedding
Planar
Testing
Planarity
Method
Subgraph
Graphs
Given
Theorem
Theory
Algorithms
K3
K5
complete graph
Planar
Testing
Planarity
Subgraph
Given
Theorem
Theory
Algorithms
K3
K5
Graphs
Time
utility graph
Planar
Testing
Planarity
Subgraph
Given
Theorem
Theory
Algorithms
K3
K5
Graphs
Time
Connections between topic areas Semantic bridges
Semantic bridges connect parts of the graph that would otherwise be more separate. A bridge is a structural signal in this analysis, not a claim that the two topic areas are equivalent.
For Planarity testing, one of the stronger structural bridges in this analysis connects Planarity testing with Algorithms. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.
Planarity testing
Nodes56
Edges55
Triples59
Avg. degree1.96
Density0.035714
Components1
Source & methodology
TTTA analyzes the structure around Planarity testing to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Science, Planarity criteria & Algorithms, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.
