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Tree-depth: Definitions, Complexity & Depth of trees and relation to treewidth

In graph theory, the tree-depth of a connected undirected graph G {\displaystyle G} is a numerical invariant of G {\displaystyle G} , the minimum height of a Trémaux tree for a supergraph of G {\displaystyle G} . This invariant and its close relatives have gone under many different names in the literature, including vertex ranking number, ordered…

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Tree-depth topic overview

The analysis highlights Definitions, Complexity and Depth of trees and relation to treewidth as prominent areas in the source structure around Tree-depth.

Related topics
46
Source areas
7
Connected nodes
53
Extracted relationships
181
Concept neighborhoods
31
Bridge connections
53

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.

Overview · 13 topics
Definitions · 11 topics
Complexity · 8 topics
Depth of trees and relation to treewidth · 6 topics
Graph minors · 3 topics
Induced subgraphs · 3 topics
Examples · 2 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

Definitions

Examples

Depth of trees and relation to treewidth

Graph minors

Induced subgraphs

Complexity

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 Tree-depth connects Entity context

The extracted context around Tree-depth shows recurring relationship patterns in the source. For example, Tree-depth → ACM, Alejandro, Alex, Algorithms, Ananth, Approximating, Archontia, Article, Aspvall, Automata, Bengt, Benjamin, BF01934264, BIT, Bodlaender, Bounded, Chapter, Cite, CiteSeerX, Combinatorics Another extracted example is Tree-depth → Any, By, Ck, For, Halin, In, More, Precisely, Since, The. Use these groups to spot repeated connection types before inspecting the individual relationships.

Tree-depth

Top relations

related to References · 147
Tree-depth → ACM, Alejandro, Alex, Algorithms, Ananth, Approximating, Archontia, Article, Aspvall, Automata, Bengt, Benjamin, BF01934264, BIT, Bodlaender, Bounded, Chapter, Cite, CiteSeerX, Combinatorics
related to Depth of trees and relation to treewidth · 10
Tree-depth → Any, By, Ck, For, Halin, In, More, Precisely, Since, The
related to Complexity · 6
Tree-depth → Bodlaender, Computing, For, NP-complete, On, The
related to Graph minors · 5
Tree-depth → If, More, Robertson, Seymour, Thus
related to Induced subgraphs · 5
Tree-depth → As, Higman's, The, Well-quasi-ordering, Within
related to Definitions · 4
Tree-depth → If, The, Thus, Trémaux
related to Examples · 3
Tree-depth → For, Similarly, The
is a · 1
Tree-depth → minimum number of colors in a centered coloring of the given graph

Important terminology

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

Important terminology

displaystyle graph graphs doi treewidth tree 10 forest height path trees may vertices time every one pebble number minimum isbn

Tree-depth relationships Subject–Predicate–Object triples

TTTA extracted 181 structured relationships around Tree-depth. Examples in this analysis include Tree-depth → is a → minimum number of colors in a centered coloring of the given graph and Tree-depth → related to Complexity → Computing. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Tree-depthis aminimum number of colors in a centered coloring of the given graph0.90text
Tree-depthrelated to ComplexityComputing0.60section
Tree-depthrelated to ComplexityNP-complete0.60section
Tree-depthrelated to ComplexityThe0.60section
Tree-depthrelated to ComplexityBodlaender0.60section
Tree-depthrelated to ComplexityOn0.60section
Tree-depthrelated to ComplexityFor0.60section
Tree-depthrelated to DefinitionsThe0.60section
Tree-depthrelated to DefinitionsIf0.60section
Tree-depthrelated to DefinitionsTrémaux0.60section
Tree-depthrelated to DefinitionsThus0.60section
Tree-depthrelated to Depth of trees and relation to treewidthAny0.60section

Related concept clusters Concept neighborhoods

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

  • graph theory
    • Tree-depth
    • Displaystyle
    • Minors
    • Treewidth
    • Height
    • Tree
    • Minimum
    • Induced
    • Number
    • Every
    • Path
    • Following
  • undirected graph
    • Tree-depth
    • Displaystyle
    • Minors
    • Treewidth
    • Height
    • Tree
    • Minimum
    • Induced
    • Number
    • Every
    • Path
    • Following
  • star height
    • Minimum
    • Tree
    • Vertex
    • Property
    • Trees
    • Every
    • May
    • Forest
    • Following
    • Minors
    • Path
    • Graphs
  • treewidth
    • Tree
    • Log
    • Graph
    • Tree-depth
    • Graphs
    • Depth
    • Property
    • Bounded
    • Displaystyle
    • One
    • May
    • Height
  • trivially perfect graph
    • Tree-depth
    • Displaystyle
    • Minors
    • Treewidth
    • Height
    • Tree
    • Minimum
    • Induced
    • Number
    • Every
    • Path
    • Following
  • graph coloring
    • Tree-depth
    • Displaystyle
    • Minors
    • Treewidth
    • Height
    • Tree
    • Minimum
    • Induced
    • Number
    • Every
    • Path
    • Following
  • complete graph
    • Tree-depth
    • Displaystyle
    • Minors
    • Treewidth
    • Height
    • Tree
    • Minimum
    • Induced
    • Number
    • Every
    • Path
    • Following
  • complete bipartite graph
    • Tree-depth
    • Displaystyle
    • Minors
    • Treewidth
    • Height
    • Tree
    • Minimum
    • Induced
    • Number
    • Every
    • Path
    • Following

Connections between topic areas Semantic bridges

For Tree-depth, one of the stronger structural bridges in this analysis connects Tree-depth with Overview. 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
Tree-depth — Overview · splits 40 ⟂ 14
Tree-depth — Definitions · splits 42 ⟂ 12
Tree-depth — Complexity · splits 45 ⟂ 9
Tree-depth — Depth of trees and relation to treewidth · splits 47 ⟂ 7
Tree-depth — Graph minors · splits 50 ⟂ 4
Tree-depth — Induced subgraphs · splits 50 ⟂ 4
Tree-depth — Examples · splits 51 ⟂ 3

Map overview Semantic statistics

Tree-depth

Nodes54
Edges53
Triples181
Avg. degree1.96
Density0.037037
Components1

Source & methodology

TTTA analyzes the structure around Tree-depth to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Definitions, Complexity & Depth of trees and relation to treewidth, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Tree-depth · EN edition · Analysis: TopicsToTalkAbout

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