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.

翻译：我们考虑一类称为厚图的图结构，其中顶点被团替换，边被二部图替换。特别地，我们研究了完美图子类中的厚森林，证明了此类图可在多项式时间内被识别，并考察了该类图中独立集与着色计数问题的复杂度。此外，我们将相关结果推广至厚森林之外的厚图。