What Makes an Algorthim Greedy [Graph Coloring Algorithm]
&quot;A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage.&quot; (from Wikipedia)  In other words, it does not backtrack.  It builds up the solution incrementally, and when it adds something to the solution-so-far, it never later removes it (or, when it makes a decision, it never later undoes that decision).
Does that describe the algorithm you are looking at?
If you want to justify that it satisfies the greedy choice property, it might help to precisely state what is the &quot;subproblem&quot; that is solved at each step.