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A hole in a graph is a chordless cycle of length at least 4. A theta is agraph formed by three paths between the same pair of distinct vertices so thatthe union of any two of the paths induces a hole. A wheel is a graph formed bya hole and a node that has at least 3 neighbors in the hole. In this series ofpapers we study the class of graphs that do not contain as an induced subgrapha theta nor a wheel. In Part II of the series we prove a decomposition theoremfor this class, that uses clique cutsets and 2-joins, and consequently obtain apolynomial time recognition algorithm for the class. In this paper we furtheruse this decomposition theorem to obtain polynomial time algorithms for maximumweight clique, maximum weight stable set and coloring problems. We also showthat for a graph $G$ in the class, if its maximum clique size is $\omega$, thenits chromatic number is bounded by max$\{\omega,3\}$, and that the class is3-clique-colorable.

The (theta, wheel)-free graphs Part III: cliques, stable sets and coloring