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Graph coloring

In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color. Graph coloring is a special case of graph labeling. In its simplest form, it is a way of coloring the vertices of a graph such…

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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

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Properties

Algorithms

Applications

Other colorings

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Graph coloring

Nodes172
Edges171
Triples117
Avg. degree1.99
Density0.011628
Components1

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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)

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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

SubjectPredicateObjectConfidenceSrc
Graph coloringApproximabilityO(n (log n)−3 (log log n)2)1.00infobox
Graph coloringApproximabilityFPRAS for restricted cases1.00infobox
Graph coloringComplexityNP-complete1.00infobox
Graph coloringComplexityNP-hard1.00infobox
Graph coloringComplexity♯P-complete1.00infobox
Graph coloringGarey–JohnsonGT41.00infobox
Graph coloringInapproximabilityO(n1−ε) unless P = NP1.00infobox
Graph coloringInapproximabilityNo PTAS unless P = NP1.00infobox
Graph coloringInputGraph G with n vertices. Integer k1.00infobox
Graph coloringInputGraph G with n vertices.1.00infobox
Graph coloringNameGraph coloring, vertex coloring, k-coloring1.00infobox
Graph coloringNameChromatic number1.00infobox
Graph coloringNameChromatic polynomial1.00infobox
Graph coloringOutputDoes G admit a proper vertex coloring with k colors?1.00infobox
Graph coloringOutputχ(G)1.00infobox
Graph coloringOutputThe number P (G, k) of proper k-colorings of G1.00infobox
Graph coloringReduction from3-Satisfiability1.00infobox
Graph coloringRunning timeO(2nn)1.00infobox
Graph coloringis amethodic assignment of labels traditionally called0.90text
Graph coloringis aspecial case of graph labeling0.90text

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