B-coloring - meaning and definition. What is B-coloring
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  3. B-coloring

What (who) is B-coloring - definition


B-coloring         
  • Example of B-coloring of [[Shrikhande graph]] with 6 colors: highlighted nodes have neighbors in each other colors. Since each node is adjacent to another 6, a 7-color B-coloring may be possible.
In graph theory, a b-coloring of a graph is a coloring of the vertices where each color class contains a vertex that has a neighbor in all other color classes.
https://en.wikipedia.org/wiki/B-coloring
graph colouring         
  • 3}}}} (blue) admits a 3-coloring; the other graphs admit a 2-coloring.
  • This graph can be 3-colored in 12 different ways.
  • Two greedy colorings of the same graph using different vertex orders. The right example generalizes to 2-colorable graphs with ''n'' vertices, where the greedy algorithm expends <math>n/2</math> colors.
ASSIGNMENT OF COLORS TO ELEMENTS OF A GRAPH SUBJECT TO CERTAIN CONSTRAINTS
Colouring algorithm; Coloring algorithm; Graph coloring algorithm; Chromatic number; Graph colouring problems; Graph coloring problem; Colored graph; Graph Colouring; Vertex chromatic number; K-vertex colorable; Vertex color; Graph colouring problem; Graph colouring; Three-Colorable Graph; Three-colorable graph; Vertex-colouring; Vertex colouring; Vertex coloring; Coloring problem; Colouring problem; Two-colorable graph; Graph two-coloring; Graph Two-Coloring; Graph coloration; Graph color; K-colouring; 3-colourability; Colourability; Proper coloring; K-coloring; Network coloring; Network colouring; K-chromatic graph; Distributed graph coloring; Cole–Vishkin algorithm; Cole-Vishkin algorithm; Mycielski's theorem; K-colorable; Unlabeled coloring; Vector chromatic number; Face coloring; Algorithms for graph coloring; Parallel algorithms for graph coloring; Applications of graph coloring; Decentralized graph coloring; Computational complexity of graph coloring
<application> A constraint-satisfaction problem often used as a test case in research, which also turns out to be equivalent to certain real-world problems (e.g. {register allocation}). Given a connected graph and a fixed number of colours, the problem is to assign a colour to each node, subject to the constraint that any two connected nodes cannot be assigned the same colour. This is an example of an NP-complete problem. See also four colour map theorem.
chromatic number         
  • 3}}}} (blue) admits a 3-coloring; the other graphs admit a 2-coloring.
  • This graph can be 3-colored in 12 different ways.
  • Two greedy colorings of the same graph using different vertex orders. The right example generalizes to 2-colorable graphs with ''n'' vertices, where the greedy algorithm expends <math>n/2</math> colors.
ASSIGNMENT OF COLORS TO ELEMENTS OF A GRAPH SUBJECT TO CERTAIN CONSTRAINTS
Colouring algorithm; Coloring algorithm; Graph coloring algorithm; Chromatic number; Graph colouring problems; Graph coloring problem; Colored graph; Graph Colouring; Vertex chromatic number; K-vertex colorable; Vertex color; Graph colouring problem; Graph colouring; Three-Colorable Graph; Three-colorable graph; Vertex-colouring; Vertex colouring; Vertex coloring; Coloring problem; Colouring problem; Two-colorable graph; Graph two-coloring; Graph Two-Coloring; Graph coloration; Graph color; K-colouring; 3-colourability; Colourability; Proper coloring; K-coloring; Network coloring; Network colouring; K-chromatic graph; Distributed graph coloring; Cole–Vishkin algorithm; Cole-Vishkin algorithm; Mycielski's theorem; K-colorable; Unlabeled coloring; Vector chromatic number; Face coloring; Algorithms for graph coloring; Parallel algorithms for graph coloring; Applications of graph coloring; Decentralized graph coloring; Computational complexity of graph coloring
<mathematics> The smallest number of colours necessary to colour the nodes of a graph so that no two adjacent nodes have the same colour. See also: four colour map theorem. {Graph Theory Lessons (http://utc.edu/chromatic numbercpmawata/petersen/lesson8.htm)}. {Eric Weisstein's World Of Mathematics (http://mathworld.wolfram.com/ChromaticNumber.html)}. {The Geometry Center (http://geom.umn.edu/chromatic numberzarembe/grapht1.html)}. (2000-03-18)
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