Graph coloring

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Map view:

Zoom: 100%

More settings

Connection length 100% Label size 100% Node size 100% Line width 100% Label width 100%

Export map as:

Graph coloring topic overview

The analysis highlights History and Applications as prominent areas in the source structure around Graph coloring.

Related topics: 162
Source areas: 7
Connected nodes: 169
Extracted relationships: 66
Related term clusters: 69
Bridge connections: 169

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 · 52 topics

Properties · 38 topics

History · 33 topics

Overview · 15 topics

Definition and terminology · 13 topics

Applications · 7 topics

Other colorings · 4 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.

Approximability: O(n (log n)−3 (log log n)2) · FPRAS for restricted cases
Complexity: NP-complete · NP-hard · ♯P-complete
Garey–Johnson: GT4
Inapproximability: O(n1−ε) unless P = NP · No PTAS unless P = NP
Input: Graph G with n vertices. Integer k · Graph G with n vertices.
Name: Graph coloring, vertex coloring, k-coloring · Chromatic number · Chromatic polynomial

Start with your topic. Discover where to go next.

Explore different angles and find fresh ideas to shape your next piece of content.

Graph coloring

3Iterated logarithm · Unit disk graph · Graph coloring

8Graph theory · Graph (discrete mathematics) · Graph labeling

5George David Birkhoff · Chromatic polynomial · Tutte polynomial

5Sharp-P-complete · Rational point · FPRAS

4NP-complete · Brooks' theorem · Four color theorem

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 and terminology

Algorithms

Applications

Other colorings

For the semantics nerds

You can skip this section if you’re here for content ideas and keyword inspiration.

Advanced semantic analysis

How Graph coloring connects Entity context

The extracted context around Graph coloring shows recurring relationship patterns in the source. For example, Graph coloring → Alfred Kempe, Arthur Cayley, Augustus De Morgan, England, Fellow, Francis Guthrie, Frederick, Guthrie's, Heawood, Kempe, Kempe's, Kenneth Appel, London Mathematical Society, Percy John Heawood, President, Royal Society, University College, William Hamilton, Wolfgang Haken Another extracted example is Graph coloring → Brooks, Graph, NP-complete, NP-hard. Use these groups to spot repeated connection types before inspecting the individual relationships.

Top relations

related to history · 19

Graph coloring → Alfred Kempe, Arthur Cayley, Augustus De Morgan, England, Fellow, Francis Guthrie, Frederick, Guthrie's, Heawood, Kempe, Kempe's, Kenneth Appel, London Mathematical Society, Percy John Heawood, President, Royal Society, University College, William Hamilton, Wolfgang Haken

related to Computational complexity · 4

Graph coloring → Brooks, Graph, NP-complete, NP-hard

related to Parallel and distributed algorithms · 4

Graph coloring → LOCAL, Omega, Schneider, Wattenhofer

Complexity · 3

Graph coloring → NP-complete, NP-hard, ♯P-complete

Name · 3

Graph coloring → Chromatic number, Chromatic polynomial, Graph coloring, vertex coloring, k-coloring

Output · 3

Graph coloring → Does G admit a proper vertex coloring with k colors?, The number P (G, k) of proper k-colorings of G, χ(G)

Approximability · 2

Graph coloring → FPRAS for restricted cases, O(n (log n)−3 (log log n)2)

Inapproximability · 2

Graph coloring → No PTAS unless P = NP, O(n1−ε) unless P = NP

Input · 2

Graph coloring → Graph G with n vertices., Graph G with n vertices. Integer k

is a · 2

Graph coloring → methodic assignment of labels traditionally called, special case of graph labeling

Important terminology

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

Important terminology

graph coloring displaystyle vertices number colors vertex color chromatic graphs polynomial edge time algorithm problem adjacent using algorithms one two

Graph coloring relationships Subject–Predicate–Object triples

TTTA extracted 66 structured relationships around Graph coloring. Examples in this analysis include Graph coloring → Approximability → O(n (log n)−3 (log log n)2) and Graph coloring → Approximability → FPRAS for restricted cases. The table shows each extracted connection, where it came from and its confidence.

Subject	Predicate	Object	Confidence	Src
Graph coloring	Approximability	O(n (log n)−3 (log log n)2)	1.00	infobox
Graph coloring	Approximability	FPRAS for restricted cases	1.00	infobox
Graph coloring	Complexity	NP-complete	1.00	infobox
Graph coloring	Complexity	NP-hard	1.00	infobox
Graph coloring	Complexity	♯P-complete	1.00	infobox
Graph coloring	Garey–Johnson	GT4	1.00	infobox
Graph coloring	Inapproximability	O(n1−ε) unless P = NP	1.00	infobox
Graph coloring	Inapproximability	No PTAS unless P = NP	1.00	infobox
Graph coloring	Input	Graph G with n vertices. Integer k	1.00	infobox
Graph coloring	Input	Graph G with n vertices.	1.00	infobox
Graph coloring	Name	Graph coloring, vertex coloring, k-coloring	1.00	infobox
Graph coloring	Name	Chromatic number	1.00	infobox
Graph coloring	Name	Chromatic polynomial	1.00	infobox
Graph coloring	Output	Does G admit a proper vertex coloring with k colors?	1.00	infobox
Graph coloring	Output	χ(G)	1.00	infobox
Graph coloring	Output	The number P (G, k) of proper k-colorings of G	1.00	infobox
Graph coloring	Reduction from	3-Satisfiability	1.00	infobox
Graph coloring	Running time	O(2nn)	1.00	infobox
Graph coloring	is a	methodic assignment of labels traditionally called	0.90	text
Graph coloring	is a	special case of graph labeling	0.90	text

Related concept clusters Related term clusters

The concept neighborhoods around Graph coloring bring nearby vocabulary together. In this analysis, examples include Graph, Vertices and Colors. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

Graph coloring
- Graph
- Vertices
- Colors
- Number
- Chromatic
- Color
- Vertex
- Displaystyle
- Polynomial
- Time
- Edge
- Graphs
graph coloring
- Graph
- Vertex
- Vertices
- Colors
- Number
- Chromatic
- Edge
- Color
- Problem
- Proper
- Displaystyle
- Polynomial
graph theory
- Vertices
- Number
- Chromatic
- Vertex
- Displaystyle
- Polynomial
- Time
- Edge
- Every
- Proper
- Algorithms
- Example
graph
- Vertices
- Number
- Chromatic
- Vertex
- Displaystyle
- Polynomial
- Time
- Edge
- Every
- Proper
- Algorithms
- Example
graph labeling
- Vertices
- Number
- Chromatic
- Vertex
- Displaystyle
- Polynomial
- Time
- Edge
- Every
- Proper
- Algorithms
- Example
vertices
- Adjacent
- Displaystyle
- Graph
- Color
- Coloring
- Vertex
- Greedy
- Colors
- Assigned
- Edge
- Edges
- Number
edge coloring
- Graph
- Vertex
- Colors
- Two
- Vertices
- Edge
- Color
- Chromatic
- Problem
- Proper
- Number
- Distributed
edge
- Two
- Chromatic
- Vertex
- Number
- Vertices
- Distributed
- Edges
- Graph
- Proper
- Displaystyle
- Problem
- Problems

Connections between topic areas Semantic bridges

For Graph coloring, one of the stronger structural bridges in this analysis connects Graph coloring 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

Graph coloring — Algorithms · splits 117 ⟂ 53

Graph coloring — Properties · splits 131 ⟂ 39

Graph coloring — History · splits 136 ⟂ 34

Graph coloring — Overview · splits 154 ⟂ 16

Graph coloring — Definition and terminology · splits 156 ⟂ 14

Graph coloring — Applications · splits 162 ⟂ 8

Graph coloring — Other colorings · splits 165 ⟂ 5

Map overview Semantic statistics

Graph coloring

Nodes170

Edges169

Triples66

Avg. degree1.99

Density0.011765

Components1

Source & methodology

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

Source: Wikipedia — Graph coloring · EN edition · Analysis: TopicsToTalkAbout

Graph coloring: History & Applications

Graph coloring topic overview

What this topic covers Research coverage

Key facts & relationships

Start with your topic. Discover where to go next.

Questions to explore

Explore all related topics Closing gaps

Overview

History

Definition and terminology

Properties

Algorithms

Applications

Other colorings

For the semantics nerds

Advanced semantic analysis

How Graph coloring connects Entity context

Graph coloring

Top relations

Important terminology

Important terminology

Graph coloring relationships Subject–Predicate–Object triples

Related concept clusters Related term clusters

Connections between topic areas Semantic bridges

Map overview Semantic statistics

Graph coloring

Source & methodology