Abstract
Graph Colouring Problem is a well-known NP-Hard problem. In Graph Colouring Problem (GCP) all vertices of any graph must be coloured in such a way that no two adjacent vertices are coloured with the same colour. In this paper, a new algorithm is proposed to solve the GCP. Proposed algorithm is based on finding vertex sets using edge cover method. In this paper implementation prospective of the algorithm is also discussed. Implemented algorithm is tested on various graph instances of DIMACS standards dataset. Algorithm execution time and a number of colours required to colour graph are compared with some other well-known Graph Colouring Algorithms. Variation in time complexity with reference to increasing in the number of vertices, a number of edges and an average degree of a graph are also discussed in this paper.
Highlights
Graph Colouring Problem is a well-known NPHard problem
When it comes to a large graph where a number of vertices and number of edges are in large number, time complexity is more important than colouring optimisation
Most of the graph colouring algorithms are tested on DIMACS graph instances
Summary
Abstract—Graph Colouring Problem is a well-known NPHard problem. In Graph Colouring Problem (GCP) all vertices of any graph must be coloured in such a way that no two adjacent vertices are coloured with the same colour. In general colouring optimisation is the primary objective of graph colouring algorithms When it comes to a large graph where a number of vertices and number of edges are in large number, time complexity is more important than colouring optimisation. For example genetic algorithm with multipoint guided mutation algorithm (MSGCA) generate optimum chromatic number (5) for graph instance 4-Insertion_4, i.e. number of colours required to colour graph of 475 vertices and 1795 edges are five. Rest of the paper is organised as follows: In section II, related work done by researchers in the field of graph colouring is discussed.
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