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A Generalization of AT-free Graphs and a Generic Algorithm for Solving Treewidth, Minimum Fill-In and Vertex Ranking

  • Hajo Broersma
  • Ton Kloks
  • Dieter Kratsch
  • Haiko Müller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1517)

Abstract

A subset A of the vertices of a graph G is an asteroidal set if for each vertex aA, the set A∖{a} is contained in one component of G-N[a]. An asteroidal set of cardinality three is called asteroidal triple and graphs without an asteroidal triple are called AT-free. The maximum cardinality of an asteroidal set of G, denoted by an(G), is said to be the asteroidal number of G. We present a scheme for designing algorithms for triangulation problems on graphs. As a consequence, we obtain algorithms to compute graph parameters such as treewidth, minimum fill-in and vertex ranking number. The running time of these algorithms is a polynomial (of degree asteroidal number plus a small constant) in the number of vertices and the number of minimal separators of the input graph.

Keywords

SIAM Journal Input Graph Chordal Graph Linear Time Algorithm Minimal Separator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Hajo Broersma
    • 1
  • Ton Kloks
    • 1
  • Dieter Kratsch
    • 2
  • Haiko Müller
    • 2
  1. 1.Faculty of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands
  2. 2.Fakultät für Mathematik und InformatikFriedrich-Schiller-UniversitätJenaGermany

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