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Induced subgraphs and well‐quasi‐ordering
Author(s) -
Damaschke Peter
Publication year - 1990
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190140406
Subject(s) - mathematics , combinatorics , induced subgraph , class (philosophy) , simple (philosophy) , cograph , chordal graph , ideal (ethics) , order (exchange) , discrete mathematics , graph , 1 planar graph , computer science , philosophy , epistemology , finance , artificial intelligence , vertex (graph theory) , economics
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 ( P 4 ‐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 P 4 ‐reducible graphs build a WQO class. Other examples of lower ideals WQO by ≤ i are also given.