  In this paper we compare and illustrate the algorithmic use of graphs of
bounded tree-width and graphs of bounded clique-width. For this purpose we give
polynomial time algorithms for computing the four basic graph parameters
independence number, clique number, chromatic number, and clique covering
number on a given tree structure of graphs of bounded tree-width and graphs of
bounded clique-width in polynomial time. We also present linear time algorithms
for computing the latter four basic graph parameters on trees, i.e. graphs of
tree-width 1, and on co-graphs, i.e. graphs of clique-width at most 2.
