The structure of (theta, pyramid, 1-wheel, 3-wheel)-free graphs
نویسندگان
چکیده
In this paper we study the class of graphs C defined by excluding the following structures as induced subgraphs: thetas, pyramids, 1-wheels and 3-wheels. 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.
منابع مشابه
The (theta, wheel)-free graphs Part I: only-prism and only-pyramid graphs
Truemper configurations are four types of graphs (namely thetas, wheels, prisms and pyramids) that play an important role in the proof of several decomposition theorems for hereditary graph classes. In this paper, we prove two structure theorems: one for graphs with no thetas, wheels and prisms as induced subgraphs, and one for graphs with no thetas, wheels and pyramids as induced subgraphs. A ...
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