A processor performs vertex coloring for a graph based at least in part on the degree of each vertex of the graph and based at least in part with another coloring approach, such as comparison of random values assigned to the vertices. For each vertex in the graph, a processor determines whether the degree of the vertex is a local maximum; that is, whether the degree of the vertex is greater than the degree of each of its connected vertices. Each vertex having a local-maximum degree is assigned a specified or randomly selected color, and is then omitted from future iterations of the coloring process. After a stop criterion is met, the processor assigns random values to the remaining uncolored vertices and assigns colors based on comparisons of the random values.