Abstract
AbstractWe 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
