Topic summary
Coloring algorithm
Extracted from the Wikipedia article Graph coloring.
Greedy coloring
For chordal graphs, and for special cases of chordal graphs such as interval graphs and indifference graphs, the greedy coloring algorithm can be used to find optimal colorings in polynomial time, by choosing the vertex ordering to be the reverse of a perfect elimination ordering for the graph. The perfectly orderable graphs generalize this property, but it is NP-hard to find a perfect ordering of these graphs.