Finding the chromatic number by means of critical graphs

We propose a new exact algorithm for finding the chromatic number of a graph G. The algorithm attempts to determine the smallest possible induced subgraph G' of G which has the same chromatic number as G. Such a subgraph is said critical since all proper induced subgraphs of G'have a chromatic number strictly smaller than G'. The proposed method is particularly helpful when a k-coloring of a non-critical graph is known, and it has to be proved that no (k-1)- coloring of G exists. Computational experiments on random graphs and on DIMACS benchmark problems demonstrate that the new proposed algorithm can solve larger problems than previous known exact methods. Key-words Chromatic number, exact algorithm, critical graphs. 

• Type: Journal
• Year: 2000
• Where: ENDM
• Authors: Francine Herrmann, Alain Hertz
• Keywords: Chromatic Number, ENDM 2000, Exact Algorithm, Possible Induced Subgraph