Linear-Time Graph Coloring Algorithm

This paper presents a novel algorithm for efficiently sampling proper colorings of a graph. The significance lies in its linear time complexity, a significant improvement over previous algorithms, especially for graphs with a high maximum degree. This advancement has implications for various applications involving graph analysis and combinatorial optimization.

• •Presents a new algorithm for sampling proper colorings of a graph.
• •Achieves linear time complexity under specific conditions.
• •Improves upon existing algorithms, especially for graphs with high maximum degree.
• •The number of colors used is linear in the maximum degree of the graph.