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Graphs of Separability at Most Two: Structural Characterizations and Their Consequences

  • Ferdinando Cicalese
  • Martin Milanič
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)

Abstract

Graphs of separability at most k are defined as graphs in which every two non-adjacent vertices are separated by a set of at most k other vertices. For k ∈ {0,1}, the only connected graphs of separability at most k are complete graphs and block graphs, respectively. For k ≥ 3, graphs of separability at most k form a rich class of graphs containing all graphs of maximum degree k. Graphs of separability at most 2 generalize complete graphs, cycles and trees. We prove several characterizations of graphs of separability at most 2 and examine some of their consequences.

Keywords

Complete Graph Internal Vertex Graph Class Free Graph Signable Graph 
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 2011

Authors and Affiliations

  • Ferdinando Cicalese
    • 1
  • Martin Milanič
    • 2
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversity of SalernoFiscianoItaly
  2. 2.FAMNIT and PINTUniversity of PrimorskaKoperSlovenia

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