# An Experimental Comparison of Heuristic Coloring Algorithms in Terms of Found Color Classes on Random Graphs

## Abstract

Well-known graph theory problems are graph coloring and finding the maximum clique in an undirected graph, or shortly - MCP. And these problems are closely related. Vertex coloring is usually considered an initial step before the start of finding maximum clique of a graph. The maximum clique problem is considered to be of NP-hard complexity, which means that there is no algorithm found that could solve this kind of problem in polynomial time. The maximum clique algorithms employ a lot the heuristic vertex coloring algorithm to find bounds and estimations. One class of such algorithms executes the coloring one only in the first stage, so those algorithms less concerned on the performance of the heuristic and more on the discovered colors. The researchers always face a problem, which heuristic vertex coloring algorithm should be selected to improve the performance of the core algorithm. Here we tried to give a lot of insights on existing heuristic vertex coloring algorithms and compare them identifying their ability to find color classes - 17 coloring algorithms are investigated: described and tested on random graphs.

## Keywords

Graph theory Vertex coloring Heuristic## References

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