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Perfect graph

In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every induced subgraph. In all graphs, the chromatic number is greater than or equal to the size of the maximum clique, but they can be far apart. A graph is perfect when these numbers are equal, and remain…

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Overview

Definitions and characterizations

History

Families of graphs

Matrices, polyhedra, and integer programming

Algorithms

Related concepts

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Perfect graph

Nodes145
Edges144
Triples115
Avg. degree1.99
Density0.013793
Components1

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Perfect graph

Top relations

related to history · 23
Perfect graph → Alfred Lehman, American Mathematical Society, Berge, Claude Berge, Fulkerson Prize, Gallai's, German, Hajnal, In, Kőnig's, Lovász, László Lovász, Maria Chudnovsky, Mathematical Optimization Society, Neil Robertson, Paul Seymour, Related, Robin Thomas, Shannon, The
related to Comparability graphs · 15
Perfect graph → An, Different, Dilworth's, Elements, Every, Finite, For, In, Its, Kőnig's, Mirsky's, Similarly, The, These, Thus
related to Algorithms · 11
Perfect graph → Because, Despite, However, In, It, Lovász, More, The, The Lovász, Then, Thus
related to Bipartite graphs and line graphs · 11
Perfect graph → By, Every, Examples, In, Induced, Kőnig's, Line, Other, The, Their, Therefore
related to Matrices, polyhedra, and integer programming · 10
Perfect graph → Although, Ax, Both, Here, NP-hard, Otherwise, Perfect, The, This, When
related to External links · 9
Perfect graph → American Institute, Graph Class Inclusions, Information System, Mathematics, Open, Perfect Problems, The Strong Perfect Graph, Theorem, Václav Chvátal
related to Split graphs and random perfect graphs · 9
Perfect graph → Almost, Hamiltonian, If, In, It, Other, The, Therefore, These
related to Families of graphs · 7
Perfect graph → Dilworth's, Examples, Kőnig's, Many, Meyniel, Mirsky's, Other
related to Strong perfection · 7
Perfect graph → Cartesian, In, Meyniel, Parity, The, The Meyniel, These
related to Definitions and characterizations · 4
Perfect graph → For, More, The, This

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Important terminology

graphs graph perfect clique number theorem vertices displaystyle induced complement bipartite two vertex set every independent also chromatic maximum strong

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Perfect graphis agraph in which the chromatic number equals the size of the maximum clique0.90text
Perfect graphrelated to AlgorithmsIn0.60section
Perfect graphrelated to AlgorithmsThe0.60section
Perfect graphrelated to AlgorithmsLovász0.60section
Perfect graphrelated to AlgorithmsThe Lovász0.60section
Perfect graphrelated to AlgorithmsThen0.60section
Perfect graphrelated to AlgorithmsDespite0.60section
Perfect graphrelated to AlgorithmsBecause0.60section
Perfect graphrelated to AlgorithmsThus0.60section
Perfect graphrelated to AlgorithmsIt0.60section
Perfect graphrelated to AlgorithmsHowever0.60section
Perfect graphrelated to AlgorithmsMore0.60section

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