Cograph

component reducible graph

An unoriented graph obtained from the single-vertex graph by the operations of disjoint union and complementation. They are characterised by having no induced subgraph $P_4$, the path of length $4$.

They are the comparability graphs of series-parallel orders.

References

• Andreas Brandstädt, Van Bang Le; Jeremy P. Spinrad, "Graph classes: a survey". SIAM Monographs on Discrete Mathematics and Applications 3. Society for Industrial and Applied Mathematics (1999) ISBN 978-0-898714-32-6 Zbl 0919.05001
• Rival, Ivan (ed.) Graphs and order. The role of graphs in the theory of ordered sets and its applications Reidel (1985) Zbl 0549.00002