We consider classes of graphs, which we call thick graphs, that have their
vertices replaced by cliques and their edges replaced by bipartite graphs. In
particular, we consider the case of thick forests, which are a subclass of
perfect graphs. We show that this class can be recognised in polynomial time,
and examine the complexity of counting independent sets and colourings for
graphs in the class. We consider some extensions of our results to thick graphs
beyond thick forests.Comment: 40 pages, 19 figure