  Truemper configurations (thetas, pyramids, prisms, and wheels) have played an
important role in the study of complex hereditary graph classes (e.g. the class
of perfect graphs and the class of even-hole-free graphs), appearing both as
excluded configurations, and as configurations around which graphs can be
decomposed. In this paper, we study the structure of graphs that contain (as
induced subgraphs) no Truemper configurations other than (possibly) universal
wheels and twin wheels. We also study several subclasses of this class. We use
our structural results to analyze the complexity of the recognition, maximum
weight clique, maximum weight stable set, and optimal vertex coloring problems
for these classes. Furthermore, we obtain polynomial chi-bounding functions for
these classes.
