Chromatic polynomial
Efficient algorithms

For some basic graph classes, closed formulas for the chromatic polynomial are known. For instance this is true for trees and cliques, as listed in the table above.

Polynomial time algorithms are known for computing the chromatic polynomial for wider classes of graphs, including chordal graphs and graphs of bounded clique-width. The latter class includes cographs and graphs of bounded tree-width, such as outerplanar graphs.
combination:two_responses