The structure of (theta, pyramid, 1-wheel, 3-wheel)-free graphs.

In this paper, we study the class of graphs C defined by excluding the following structures as induced subgraphs: theta, pyramid, 1-wheel, and 3-wheel. We describe the structure of graphs in C, and we give a polynomial-time recognition algorithm for this class. We also prove that K4-free graphs in C are 4-colorable. We remark that C includes the class of chordal graphs, as well as the class of line graphs of triangle-free graphs.