INDUCED SUBGRAPHS AND WELL-QUASI-ORDERING

We study classes of finite, simple, undirected graphs that are (1) lower ideals (or hereditary) in the partial order of graphs by the induced subgraph relation ≤i, and (2) well‐quasi‐ordered (WQO) by this relation. The main result shows that the class of cographs (P4‐free graphs) is WQO by ≤i, and that this is the unique maximal lower ideal with one forbidden subgraph that is WQO. This is a consequence of the famous Kruskal theorem. Modifying our idea we can prove that P4‐reducible graphs build a WQO class. Other examples of lower ideals WQO by ≤i are also given. Copyright © 1990 Wiley Periodicals, Inc., A Wiley Company