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Pathwidth: Characters & Applications

In graph theory, a path decomposition of a graph G is, informally, a representation of G as a "thickened" path graph, and the pathwidth of G is a number that measures how much the path was thickened to form G. More formally, a path-decomposition is a sequence of subsets of vertices of G such that the endpoints of each edge appear in one of the subsets…

Language: English [EN]
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Pathwidth topic overview

The analysis highlights Characters and Applications as prominent areas in the source structure around Pathwidth.

Related topics
88
Source areas
7
Connected nodes
95
Extracted relationships
88
Concept neighborhoods
47
Bridge connections
95

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.

Bounds · 22 topics
Overview · 21 topics
Applications · 19 topics
Graph minors · 10 topics
Computing path-decompositions · 7 topics
Alternative characterizations · 6 topics
Definition · 3 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.

Explore all related topics Closing gaps

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.

Overview

Definition

Alternative characterizations

Bounds

Computing path-decompositions

Graph minors

Applications

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Pathwidth connects Entity context

The extracted context around Pathwidth shows recurring relationship patterns in the source. For example, Pathwidth → But, For, If, In, K3, K5, Robertson, Seymour, Specifically, Then, Wagner's, X-minor-free, X-minor-free-graphs Another extracted example is Pathwidth → Although Xp, Based, Contraction, For, However, K3, The, Therefore, X0, X1, X2, Xp. Use these groups to spot repeated connection types before inspecting the individual relationships.

Pathwidth

Top relations

related to Excluding a forest · 13
Pathwidth → But, For, If, In, K3, K5, Robertson, Seymour, Specifically, Then, Wagner's, X-minor-free, X-minor-free-graphs
related to Obstructions to bounded pathwidth · 12
Pathwidth → Although Xp, Based, Contraction, For, However, K3, The, Therefore, X0, X1, X2, Xp
related to Approximation algorithms · 7
Pathwidth → Bodlaender, For, Guha, It, Kloks, NP-hard, The
related to Compiler design · 6
Pathwidth → An, DAG, For, In, It, Once
related to Exponential algorithms · 6
Pathwidth → For, Many, NP-hard, On, Such, The
related to Special classes of graphs · 6
Pathwidth → Bodlaender, Determining, Halin, However, It, NP-complete
related to Vertex separation number · 6
Pathwidth → And, Ellis, Sudborough, The, This, Turner
related to Bounds · 5
Pathwidth → Every, For, In, Since, The
related to Interval thickness · 5
Pathwidth → In, Its, That, The, Then
related to Computing path-decompositions · 4
Pathwidth → It, Nevertheless, NP-complete, The

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

graph graphs number vertex vertices one bounded interval path decomposition linear may two time also separation algorithms treewidth edge set

Pathwidth relationships Subject–Predicate–Object triples

TTTA extracted 88 structured relationships around Pathwidth. Examples in this analysis include Pathwidth → related to Alternative characterizations → As Bodlaender and Pathwidth → related to Approximation algorithms → It. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Pathwidthrelated to Alternative characterizationsAs Bodlaender0.60section
Pathwidthrelated to Approximation algorithmsIt0.60section
Pathwidthrelated to Approximation algorithmsNP-hard0.60section
Pathwidthrelated to Approximation algorithmsThe0.60section
Pathwidthrelated to Approximation algorithmsFor0.60section
Pathwidthrelated to Approximation algorithmsBodlaender0.60section
Pathwidthrelated to Approximation algorithmsGuha0.60section
Pathwidthrelated to Approximation algorithmsKloks0.60section
Pathwidthrelated to BoundsEvery0.60section
Pathwidthrelated to BoundsIn0.60section
Pathwidthrelated to BoundsSince0.60section
Pathwidthrelated to BoundsThe0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Pathwidth bring nearby vocabulary together. In this analysis, examples include Graphs, Bounded and Time. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Pathwidth
    • Graphs
    • Bounded
    • Time
    • Vertex
    • Treewidth
    • Vertices
    • Algorithms
    • Known
    • Also
    • Size
    • Minors
    • May
  • pathwidth
    • Graphs
    • Bounded
    • Time
    • Vertex
    • Treewidth
    • Vertices
    • Algorithms
    • Known
    • Also
    • Size
    • Minors
    • May
  • graph theory
    • Pathwidth
    • Number
    • Vertices
    • Graphs
    • Interval
    • Bounded
    • One
    • Edges
    • Vertex
    • Two
    • Path
    • Clique
  • graph
    • Pathwidth
    • Number
    • Vertices
    • Graphs
    • Interval
    • Bounded
    • One
    • Edges
    • Vertex
    • Two
    • Path
    • Clique
  • path graph
    • Pathwidth
    • Width
    • Number
    • Vertices
    • One
    • Graphs
    • Interval
    • Bounded
    • Way
    • May
    • Edges
    • Vertex
  • maximum clique
    • Interval
    • Maximal
    • Less
    • Size
    • One
    • Number
    • Clique
    • Given
    • Maximum
    • Width
    • Set
    • Vertices
  • interval
    • Clique
    • Number
    • One
    • Path
    • Less
    • Way
    • Width
    • Vertex
    • Treewidth
    • Maximum
    • Ordering
    • May
  • graph minors
    • Pathwidth
    • Number
    • Vertices
    • Graphs
    • Set
    • Forest
    • Interval
    • Bounded
    • One
    • Edges
    • Vertex
    • Two

Connections between topic areas Semantic bridges

For Pathwidth, one of the stronger structural bridges in this analysis connects Pathwidth with Bounds. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Pathwidth — Bounds · splits 73 ⟂ 23
Pathwidth — Overview · splits 74 ⟂ 22
Pathwidth — Applications · splits 76 ⟂ 20
Pathwidth — Graph minors · splits 85 ⟂ 11
Pathwidth — Computing path-decompositions · splits 88 ⟂ 8
Pathwidth — Alternative characterizations · splits 89 ⟂ 7
Pathwidth — Definition · splits 92 ⟂ 4

Map overview Semantic statistics

Pathwidth

Nodes96
Edges95
Triples88
Avg. degree1.98
Density0.020833
Components1

Source & methodology

TTTA analyzes the structure around Pathwidth to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Characters & Applications, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Pathwidth · EN edition · Analysis: TopicsToTalkAbout

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