Comparing the Best Maximum Clique Finding Algorithms, Which are Using Heuristic Vertex Colouring

In this paper two best known at the moment algorithms for finding the maximum clique is compared. A key technique that both algorithms rely on is using a heuristic vertex colouring. The only difference between those algorithms is a way of using vertex-colouring and this difference in the very important. The algorithms’ approaches are divided in this paper into two classes: reapplying vertex colouring on each depth and re-using colour classes obtained before the start of the main part. Historical attempts to use the colour classes for the maximum clique finding are also reviewed. Those two algorithms were never compared so far as is not widely announced also. The comparison is essential information for finding further development ways. Key-Words: maximum clique, vertex colouring, graph theory