Finding the chromatic number by means of critical graphs

10 years 6 months ago
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.
Francine Herrmann, Alain Hertz
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2000
Where ENDM
Authors Francine Herrmann, Alain Hertz
Comments (0)