Graph extremities and minimal separation
نویسنده
چکیده
A. Berry Abstra t: Many problems related to knowledge dis overy an be modelized by an undire ted graph, whi h in turn has a strong stru ture asso iated with its minimal separators. On several well-known graph lasses whi h are used in appli ations, the graph extremities and the related elimination orderings are an eÆ ient algorithmi tool. Often, these extremities turn out to be related to the minimal separators of the graph. We examine this relationship on hordal graphs, weakly hordal graphs, hordal probe graphs, unbreakable graphs and obipartite graphs, as well as on arbitrary graphs. We show that there are two kinds of extremities: verti es whose neighborhood is a minimal separator (we all these strong extremities) and verti es whose neighborhood looks like a minimal separator (we all these weak extremities).
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