An FPTAS for Counting Proper Four-Colorings on Cubic Graphs

Graph coloring is arguably the most exhaustively studied problem in the area of approximate counting. It is conjectured that there is a fully polynomial-time (randomized) approximation scheme (FPTAS/FPRAS) for counting the number of proper colorings as long as q ≥ ∆ + 1, where q is the number of colors and ∆ is the maximum degree of the graph. The bound of… CONTINUE READING