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Cograph

In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation and disjoint union. That is, the family of cographs is the smallest class of graphs that includes K1 and is closed under complementation and disjoint union.

Computational properties, Definition & Overview

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Overview

Definition

Cotrees

Computational properties

Enumeration

  • OEIS On-Line Encyclopedia of Integer Sequences

Related graph families

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Map overview Semantic statistics

Cograph

Nodes65
Edges64
Triples41
Avg. degree1.97
Density0.030769
Components1

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Cograph

Top relations

related to Computational properties · 11
Cograph → Because, Cographs, Courcelle's, For, Hamiltonian, Hamiltonicity, LexBFS, MSO1, Once, Similar, Thus
related to Subclasses · 6
Cograph → Every, Its, Ka, Kn, Similarly, Turán
related to External links · 4
Cograph → Eric, Graph Class InclusionsWeisstein, Information System, MathWorld
related to Other characterizations · 4
Cograph → Among, P4, Several, That
related to Superclasses · 4
Cograph → In, P4-free, The, Thus
is a · 3
Cograph → graph all of whose induced subgraphs have the property that any maximal clique intersects any maximal independent set in a single vertex.A cograph is a graph in which every nont…, graph which does not contain the path P4 on 4 vertices, perfect order which further implies that max clique finding and min colouring can be found in linear time with any greedy colouring and without the need for a cotree decompositi…
related to Cotrees · 2
Cograph → Alternatively, Every
related to Enumeration · 2
Cograph → For, The
related to Recursive construction · 1
Cograph → Any

Important terminology Word statistics

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Important terminology

graph cographs every graphs cotree induced union clique subgraph may vertices disjoint labeled one two time also maximum perfect vertex

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cographis agraph which does not contain the path P4 on 4 vertices0.90text
Cographis agraph all of whose induced subgraphs have the property that any maximal clique intersects any maximal independent set in a single vertex.A cograph is a graph in which every nont…0.90text
Cographis aperfect order which further implies that max clique finding and min colouring can be found in linear time with any greedy colouring and without the need for a cotree decompositi…0.90text
finding a maximum clique that are hard on more general graph classes.Special types of cograph include complete graphsinstance ofThey have a simple structural decomposition involving disjoint union and complement graph operations that can be represented concisely by a labeled tree and used algorithmically…0.80text
complete bipartite graphsinstance ofThey have a simple structural decomposition involving disjoint union and complement graph operations that can be represented concisely by a labeled tree and used algorithmically…0.80text
cluster graphsinstance ofThey have a simple structural decomposition involving disjoint union and complement graph operations that can be represented concisely by a labeled tree and used algorithmically…0.80text
and threshold graphsinstance ofThey have a simple structural decomposition involving disjoint union and complement graph operations that can be represented concisely by a labeled tree and used algorithmically…0.80text
Cographrelated to Computational propertiesCographs0.60section
Cographrelated to Computational propertiesLexBFS0.60section
Cographrelated to Computational propertiesOnce0.60section
Cographrelated to Computational propertiesFor0.60section
Cographrelated to Computational propertiesThus0.60section

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    Min side: 3
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