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)


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.


Complete Graph Internal Vertex Graph Class Free Graph Signable Graph 
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© 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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