Solving Hard Computational Problems Efficiently: Asymptotic Parametric Complexity 3-Coloring Algorithm
The behavior of the proposed algorithm over the well-known Erdős-Rënyi random graphs distribution. Plot (a) shows the quantity of 3-colorable and non-3-colorable graphs as a function of the average degree, i.e., a phase transition plot, in this case, occurring at around . Plot (b) shows the quantity of graphs corresponding to each value. As predicted by the theory, the proportion of graphs decreases exponentially as a function of below the line of . Plots (c) and (d) show the running times as a function of the average degree.