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Explore the main themes, entities and connections around Graph coloring. Start with the topic map, then use the sections below for research and deeper semantic analysis.
Explore this topic
Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.
History
34 related topics
Properties
39 related topics
Algorithms
52 related topics
Definition and terminology
13 related topics
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
Topics to explore
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.Browse the full topic structure. Each item opens a new analysis centered on that subject.
Overview
- Graph theory
- Graph Graph (discrete mathematics)
- Graph labeling
- Vertices Vertex (graph theory)
- Edge coloring
- Edge Edge (graph theory)
- Planar graph
- Face Face (graph theory)
- Line graph
- Dual Dual graph
- Pedagogical Pedagogy
- Political map
- Embedded Graph embedding
- Finite set
- Sudoku
History
- Planar graphs
- Map coloring
- Francis Guthrie
- Four color conjecture
- Frederick Frederick Guthrie (scientist)
- Augustus De Morgan
- University College University College London
- William Hamilton William Rowan Hamilton
- Arthur Cayley
- London Mathematical Society
- Alfred Kempe
- Royal Society
- Percy John Heawood
- Five color theorem
- Kenneth Appel
- Wolfgang Haken
- Computer-aided proof
- George David Birkhoff
- Chromatic polynomial
- Tutte polynomial
- W. T. Tutte
- Algebraic graph theory
- Claude Berge
- Information-theoretic Information theory
- Zero-error capacity Zero-error capacity?action=edit&redlink=1
- Shannon Claude Shannon
- Strong perfect graph theorem
- Chudnovsky Maria Chudnovsky
- Robertson Neil Robertson (mathematician)
- Seymour Paul Seymour (mathematician)
Definition and terminology
- Loop Loop (graph theory)
- Integers Integer
- Euler characteristic
- Independent set Independent set (graph theory)
- Polynomial
- Matchings Matching (graph theory)
- Cubic graph
- Four color theorem
- Bridgeless Bridge (graph theory)
- William T. Tutte
- Orbit Group action (mathematics)
- Automorphism group Graph automorphism
- Permutation
Properties
- Edgeless graphs Edgeless graph
- Complete graph
- Χ-bounded
- Clique number
- Bipartite graphs Bipartite graph
- Trees Tree (graph theory)
- Greedy coloring
- Degree Degree (graph theory)
- Odd cycles Odd cycle
- Brooks' theorem
- Cliques Clique (graph theory)
- Perfect graphs Perfect graph
- Clique problem
- Lovász number
- Fractional chromatic number
- Grötzsch graph
- Mycielskians Mycielskian
- AlexanderZykov Alexander Zykov?action=edit&redlink=1
- JanMycielski Jan Mycielski
- Triangle-free graphs Triangle-free graph
- Intersection graph
- Girth Girth (graph theory)
- Erdős Paul Erdős
- Kőnig's theorem Kőnig's theorem (graph theory)
- Vizing's Theorem: Vizing's theorem
- Acyclic orientation
- Longest path
- Gallai–Hasse–Roy–Vitaver theorem
- Nowhere-zero flows
- Infinite graph
Algorithms
- Linear time
- Breadth-first search
- Depth-first search
- Polynomial time
- Semidefinite programming
- Closed formulas Closed-form expression
- Branch-decomposition
- Brute-force search
- Dynamic programming
- Maximal independent set
- Inclusion–exclusion
- Yates Frank Yates
- Contraction Contraction (graph theory)
- Recurrence relation
- Fibonacci numbers
- Spanning trees Spanning tree (mathematics)
- Branch and bound
- Graph isomorphism Isomorphism
- Greedy algorithm
- Crown graph
- Chordal graphs Chordal graph
- Interval graphs Interval graph
- Indifference graphs Indifference graph
- Perfect elimination ordering
- Perfectly orderable graphs Perfectly orderable graph
- Brélaz Daniel Brélaz
- Grundy number
- DSatur
- Recursive largest first algorithm
- Graph Graph (graph theory)
Applications
- Scheduling problems Scheduling (computing)
- Bandwidth allocation
- Compiler
- Computer program
- Computer language
- Compiler optimization
- Processor registers Processor register
Other colorings
- Ramsey theory
- Theorem on friends and strangers
- Signed graphs Signed graph
- Gain graphs Gain graph
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.
Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.Graph coloring
Nodes172
Edges171
Triples117
Avg. degree1.99
Density0.011628
Components1
How this topic connects Entity context
Quick relationship hints grouped by predicate. Useful for spotting recurring semantic connections around the current entity.See the strongest relationship patterns around the current topic before diving into the raw triples.
Graph coloring
Top relations
related to history · 24
Graph coloring → Alfred Kempe, Arthur Cayley, Augustus De Morgan, England, Fellow, For, Francis Guthrie, Frederick, Guthrie's, Heawood, However, In, Kempe, Kempe's, Kenneth Appel, London Mathematical Society, Percy John Heawood, President, Royal Society, The
related to External links · 23
Graph coloring → Algorithms, Applications, Archived, Chromatic, CoLoRaTiOn, David, Flow Polynomials Archived, Gary Haggard, GCol An, Gordon RoyleA, Graph Colouring, Guide, High-Performance Graph Colouring Algorithms, Jim Andrews, Jose Antonio Martin, Mike Fellows, Pearce, Springer International Publishers, Suite, Tutte
related to Computational complexity · 11
Graph coloring → Brooks, For, Further, Graph, However, In, It, NP-complete, NP-hard, On, The
related to Parallel and distributed algorithms · 8
Graph coloring → In, It, LOCAL, Omega, Schneider, The, This, Wattenhofer
related to Decentralized algorithms · 4
Graph coloring → Decentralized, SINR, These, This
related to Modular Coloring · 4
Graph coloring → First, In, Let, Modular
related to Register allocation · 4
Graph coloring → Ideally, If, The, To
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)
Important terminology Word statistics
Frequent words and multi-word phrases across the lead, headings, infobox and body. Useful for terminology coverage.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
Entity relationships Subject–Predicate–Object triples
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| 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 |
No triples extracted yet.
Related concept clusters Concept neighborhoods
Clusters of nearby vocabulary surrounding the topic. Scan them for adjacent concepts and language you may have missed.These clusters group vocabulary that occurs around closely connected concepts in the source material.
Connections between topic areas Semantic bridges
Bridge nodes connect otherwise separate parts of the map. Expand a row to inspect the topic groups on each side.Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.
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