In Graph Theory
In graph theory, a hereditary property is a property of a graph which also holds for (is "inherited" by) its induced subgraphs. Alternately, a hereditary property is preserved by the removal of vertices. A graph class is said hereditary if it is closed under induced subgraphs. Examples of hereditary graph classes are independent graphs (graphs with no edges), which is a special case (with c = 1) of being c-colorable for some number c, being forests, planar, complete, complete multipartite etc.
In some cases, the term "hereditary" has been defined with reference to graph minors, but this is more properly called a minor-hereditary property. The Robertson–Seymour theorem implies that a minor-hereditary property may be characterized in terms of a finite set of forbidden minors.
Read more about this topic: Hereditary Property
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