Choosability in coloring problems of graphs with restricted color lists

In this paper we present a correlation between a variation of the list problem coloring in graphs, the (γ, μ)-coloring, and the property of choosability in graphs, resulting in the k-(γ, μ)-choosability. The list coloring problem is a variation of the classical vertex coloring problem, introduced by Erdos et al. in 1979, along with a property very studied in list coloring: the choosability in graphs. In this work, algorithms were developed to determine the k-choosability and the k-(γ, μ)-choosability of a general simple graph, and a greedy heuristic based on DSATUR. In addition, we applied special techniques to prove the property of choosability in some classes of graphs, involving a general proof for simple graphs, which guarantees that if a graph is k-colorable it is also k-(Y, μ)-choosable, being the computational complexity reduced from the class Π
²
p
-complete to the NP-complete.