Perfect elimination scheme

Perfect elimination scheme --- совершенная схема удаления.

Let [math]\displaystyle{ G = (V,E) }[/math] be a graph. A simplicial vertex of [math]\displaystyle{ G }[/math] is a vertex of which the neighborhood induces a clique. An ordering of the vertices [math]\displaystyle{ \sigma = (v_{1}, \ldots, v_{n}) }[/math] is called a perfect elimination scheme if for every [math]\displaystyle{ 1 \leq i \leq n }[/math], [math]\displaystyle{ v_{i} }[/math] is a simplicial vertex in [math]\displaystyle{ G[v_{i}, \ldots, v_{n}] }[/math].

A graph [math]\displaystyle{ G }[/math] is a perfect elimination graph (or chordal graph) if and only if there exists a perfect elimination scheme for [math]\displaystyle{ G }[/math].