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Clique problem: History, Applications & Science

In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph. It has several different formulations depending on which cliques, and what information about the cliques, should be found. Common formulations of the clique problem include…

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Clique problem topic overview

The analysis highlights History, Applications and Science as prominent areas in the source structure around Clique problem.

Related topics
132
Source areas
5
Connected nodes
137
Extracted relationships
117
Concept neighborhoods
57
Bridge connections
137

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 · 56 topics
Lower bounds · 29 topics
Overview · 23 topics
History and applications · 16 topics
Definitions · 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.

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

History and applications

Definitions

Algorithms

Lower bounds

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 Clique problem connects Entity context

The extracted context around Clique problem shows recurring relationship patterns in the source. For example, Clique problem → Also, But, Cook, Erdős, Feige, For, Harary, In, Karp, Luce, Many, NP, NP-completeness, Perry, Ramsey, Ross, See, Since, Social, Szekeres Another extracted example is Clique problem → Because, Boolean, CNF, Cook, From, If, It, Karp, Karp's NP-completeness, Levin, NP-complete, NP-hard, Reducibility Among Combinatorial Problems, Richard Karp's, Satisfiability, Stephen Cook's, That, The, Therefore, This. Use these groups to spot repeated connection types before inspecting the individual relationships.

Clique problem

Top relations

related to history · 24
Clique problem → Also, But, Cook, Erdős, Feige, For, Harary, In, Karp, Luce, Many, NP, NP-completeness, Perry, Ramsey, Ross, See, Since, Social, Szekeres
related to NP-completeness · 21
Clique problem → Because, Boolean, CNF, Cook, From, If, It, Karp, Karp's NP-completeness, Levin, NP-complete, NP-hard, Reducibility Among Combinatorial Problems, Richard Karp's, Satisfiability, Stephen Cook's, That, The, Therefore, This
related to Hardness of approximation · 17
Clique problem → After, An, Boolean, Depending, False, For, Garey, However, If, In, Johnson, NP, NP-complete, NP-hard, The, They, Weak
related to Finding maximum cliques in arbitrary graphs · 15
Clique problem → Bron, DIMACS, DNA, However, It, Jian, Kerbosch, Non-standard, Robson, Robson's, Tarjan, The, There, These, Trojanowski
related to Fixed-parameter intractability · 12
Clique problem → Although, Because, Cook, Downey, Fellows, For, Levin, Moreover, Parameterized, That, They, Thus
related to Special classes of graphs · 11
Clique problem → Conversely, Even, For, However, In, Kuratowski's, Kőnig's, Lempel, Perfect, Planar, Pnueli
related to Approximation algorithms · 7
Clique problem → Although, Boppana, By, Feige, Halldórsson, Several, The
related to Circuit complexity · 6
Clique problem → Additionally, Because, Even, However, NOT, The
is a · 2
Clique problem → computational problem of finding cliques, special case in which all weights are equal

Important terminology

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

Important terminology

clique problem cliques graph algorithm maximal time maximum vertices graphs number algorithms finding size one also possible decision polynomial problems

Clique problem relationships Subject–Predicate–Object triples

TTTA extracted 117 structured relationships around Clique problem. Examples in this analysis include Clique problem → is a → computational problem of finding cliques and Clique problem → is a → special case in which all weights are equal. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Clique problemis acomputational problem of finding cliques0.90text
Clique problemis aspecial case in which all weights are equal0.90text
theirs in which the running time depends on the output size is known as an output-sensitive algorithminstance ofAn algorithm0.80text
the Boolean satisfiability probleminstance ofNP.The rough idea of these inapproximability results is to form a graph that represents a probabilistically checkable proof system for an NP-complete problem0.80text
Clique problemrelated to Approximation algorithmsSeveral0.60section
Clique problemrelated to Approximation algorithmsAlthough0.60section
Clique problemrelated to Approximation algorithmsFeige0.60section
Clique problemrelated to Approximation algorithmsBy0.60section
Clique problemrelated to Approximation algorithmsBoppana0.60section
Clique problemrelated to Approximation algorithmsHalldórsson0.60section
Clique problemrelated to Approximation algorithmsThe0.60section
Clique problemrelated to Circuit complexityThe0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Clique problem bring nearby vocabulary together. In this analysis, examples include Problem, Maximum and Maximal. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Clique problem
    • Problem
    • Maximum
    • Maximal
    • Graph
    • Cliques
    • Vertices
    • Graphs
    • Algorithm
    • Input
    • Time
    • Number
    • One
  • clique problem
    • Problem
    • Maximum
    • Maximal
    • Graph
    • Cliques
    • Vertices
    • Graphs
    • Algorithm
    • Input
    • Time
    • Number
    • One
  • cliques
    • Maximal
    • Listing
    • Time
    • Graphs
    • Finding
    • Number
    • Size
    • Maximum
    • Polynomial
    • Algorithm
    • Graph
    • Possible
  • graph
    • Algorithm
    • Input
    • Number
    • Problem
    • Edges
    • Maximum
    • Vertices
    • Every
    • Vertex
    • Possible
    • One
    • Size
  • maximum clique
    • Problem
    • Maximum
    • Maximal
    • Graph
    • Graphs
    • Cliques
    • Vertices
    • Algorithm
    • Using
    • Time
    • Number
    • One
  • maximal cliques
    • Maximal
    • Listing
    • Time
    • Graphs
    • Finding
    • Number
    • Size
    • Maximum
    • Polynomial
    • Possible
    • Algorithm
    • Graph
  • decision problem
    • Complexity
    • Maximum
    • Graph
    • Size
    • Graphs
    • Input
    • Time
    • Decision
    • Problem
    • Case
    • Problems
    • Number
  • vertices
    • Edges
    • Number
    • Clique
    • Graph
    • Maximum
    • Set
    • One
    • Graphs
    • Algorithm
    • Maximal
    • Vertex
    • Cliques

Connections between topic areas Semantic bridges

For Clique problem, one of the stronger structural bridges in this analysis connects Clique problem 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.

Min side: 3
Clique problem — Algorithms · splits 81 ⟂ 57
Clique problem — Lower bounds · splits 108 ⟂ 30
Clique problem — Overview · splits 114 ⟂ 24
Clique problem — History and applications · splits 121 ⟂ 17
Clique problem — Definitions · splits 129 ⟂ 9

Map overview Semantic statistics

Clique problem

Nodes138
Edges137
Triples117
Avg. degree1.99
Density0.014493
Components1

Source & methodology

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

Source: Wikipedia — Clique problem · EN edition · Analysis: TopicsToTalkAbout

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