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This is a Experimental Study study.

Influence of the graph density on approximate algorithms for the graph vertex coloring problem

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This analysis reveals how graph density affects solutions in graph coloring, indicating implications for algorithm performance.

The first algorithm generally produced better solutions compared to the second, showing a clear performance difference.
As graph density exceeds 85%, the number of required colors increases significantly for both algorithms, impacting efficiency.
Execution times were measured by running each algorithm on the test applications six times across various graph densities.
Identical solutions were produced by both algorithms when graph density surpassed 97%, challenging assumptions about distinct algorithm performance.

Kralev et al. (2025) studied this question.

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