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In this paper we introduce the concept of a boundary class, which is a helpful tool for classification of hereditary classes of graphs according to the complexity of the independent set problem. It is shown that in a class X defined by a finite set of forbidden induced subgraphs, the problem is...
A maximum stable set in a graph G is a stable set of maximum size. S is a local maximum stable set of G , and we write S ∈Ψ( G ), if S is a maximum stable set of the subgraph spanned by S ∪ N ( S ), where N ( S ) is the neighborhood of S . A matching M is uniquely restricted if its saturated...
We introduce some large classes of P 5 -free graphs for which the maximum stable set problem can be efficiently solved. The solution algorithms are based on the search of augmenting vertices. Then a method for extending some of them to the weighted case is provided.
The struction method is a general approach to compute the stability number of a graph based on step-by-step transformations each of which reduces the stability number by exactly one. This approach has been originally derived from Boolean arguments and has been applied by different authors to...
The maximum stable set problem is NP-hard, even when restricted to banner -free graphs. In this paper, we use the augmenting graph approach to attack the problem in two subclasses of banner -free graphs. We first provide both classes with the complete characterization of minimal augmenting...
We define a hereditary system on a finite set U as a partition of the family 2 U of all subsets of U into disjoint families A and D satisfying (A∈ A ,A′⊆A)⇒A′∈ A and (D∈ D ,D⊆D′)⇒D′∈ D , respectively. The members of A are called independent sets, the sets D∈ D are called...
A graph G is said to be well-covered if every maximal independent set of vertices has the same cardinality. A planar (simple) graph in which each face is a triangle is called a triangulation . It is the aim of this paper to prove that there are no 5-connected planar well-covered triangulations.
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