Graph Colouring

Problem Description

A graph is a set of nodes and a symmetric, binary link relation on nodes. Given a set of N colours, a graph is colourable if each node can be assigned a colour in such a way that any two nodes that are linked together cannot have the same colour.

Predicates

• Input: node/1, link/2, colour/1

• Output: chosenColour/2

Input format

A number of node facts which give the names of the nodes. Node names are consecutive, ascending integers starting from 1.

A number of colour facts which give the names of the colours. Colour names start with the sequence "red", "green", "blue".

A number of link facts which say which nodes are linked. Note that if link(N1,N2). is included then so will link(N2,N1).

Output format

A set of choosenColour predicates, one for each node, specifying the node's colour.

Example(s)

Given the following input:

node(1). node(2). node(3). 
link(1,2). link(2,1). link(2,3). 
link(3,2). link(3,1). link(1,3). 
colour(red). colour(green). colour(blue).

Resulting in the output:

chosenColour(1,red). chosenColour(2,green). chosenColour(3,blue).

Additional sample instances: download

Problem Peculiarities

Type: Search Competition: System Track Complexity: NP-complete

Notes and updates

Instances taken from the 2009 competition (60 instances).

Author(s)

• Author: Johannes Wallner
  • Affiliation: DBAI, Vienna University of Technology, Austria
• Original Authors: Yuliya Lierler, Marcello Balduccini
  • Affiliation: University of Kentucky and Kodak Research Labs