Hereditary class of graphs

Hereditary class of graphs --- наследственный класс графов.

Let [math]\displaystyle{ ISub(G) }[/math] be the set of all induced subgraphs of a graph [math]\displaystyle{ G }[/math]. A class of graphs [math]\displaystyle{ P }[/math] is called hereditary class of graphs, if [math]\displaystyle{ ISub(G) \subseteq P }[/math] for every [math]\displaystyle{ G \in P }[/math]. The following hereditary class is associated with any class [math]\displaystyle{ Q }[/math]: [math]\displaystyle{ Perf(Q) = \{G: \; ISub(G) \subseteq Q\}. }[/math] For example, if [math]\displaystyle{ Q = \{G: \; i(G) = \gamma(G)\} }[/math], then [math]\displaystyle{ Perf(Q) }[/math] is a well-known class of domination perfect graphs, which was defined by Sumner and Moore in 1979 and characterized in terms of 17 forbidden induced subgraphs.