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Complete coloring

In graph theory, a complete coloring is a (proper) vertex coloring in which every pair of colors appears on at least one pair of adjacent vertices. Equivalently, a complete coloring is minimal in the sense that it cannot be transformed into a proper coloring with fewer colors by merging pairs of color classes. The achromatic number ψ(G) of a graph G is…

Complexity theory, Special classes of graphs & Algorithms

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Complexity theory

Optimization problem Decision problem Partition Disjoint sets Independent set

7 related topics

Special classes of graphs

Bipartite graphs Complements Cographs Interval graphs Hypercube graph

5 related topics

Algorithms

Approximation ratio

1 related topics

Overview

Graph theory Vertex coloring Vertices Harmonious coloring

4 related topics

Topics to explore

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Overview

Graph theory
Vertex coloring Graph coloring
Vertices Vertex (graph theory)
Harmonious coloring

Complexity theory

Optimization problem
Decision problem
Partition Partition of a set
Disjoint sets
Independent set Independent set (graph theory)
NP-hard
NP-complete

Algorithms

Approximation ratio

Special classes of graphs

Bipartite graphs Bipartite graph
Complements Graph complement
Cographs Cograph
Interval graphs Interval graph
Hypercube graph

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Complete coloring

Nodes22

Edges21

Triples8

Avg. degree1.91

Density0.090909

Components1

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Complete coloring

Top relations

related to Complexity theory · 7

Complete coloring → Determining, Finding, Gavril, NP-complete, NP-hard, The, Yannakakis

is a · 1

Complete coloring → opposite of a harmonious coloring

Important terminology Word statistics

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Important terminology

complete coloring number colors achromatic graph vertices problem classes proper every pair one adjacent theory optimization trees least possible harmonious

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Complete coloring	is a	opposite of a harmonious coloring	0.90	text
Complete coloring	related to Complexity theory	Finding	0.60	section
Complete coloring	related to Complexity theory	The	0.60	section
Complete coloring	related to Complexity theory	Determining	0.60	section
Complete coloring	related to Complexity theory	NP-hard	0.60	section
Complete coloring	related to Complexity theory	NP-complete	0.60	section
Complete coloring	related to Complexity theory	Yannakakis	0.60	section
Complete coloring	related to Complexity theory	Gavril	0.60	section

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Min side: 3

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