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Solving Hard Computational Problems Efficiently: Asymptotic Parametric Complexity 3-Coloring Algorithm

Figure 6

Runtime analysis of the algorithm for random graphs.

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.

Figure 6