Characterizing and Recognizing Probe Block Graphs

Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 20)


Block graphs are graphs in which every block (biconnected component) is a clique. A graph G = (V,E) is said to be an (unpartitioned) probe block graph if there exists an independent set ℕ ⊆ V and some set \(E' \subseteq \binom{\mathbb{N}}{2}\) such that the graph G′ = (V,E ∪ E′) is a block graph; if an independent set ℕ is given, G is called a partitioned block graph. In this note we give good characterizations for probe block graphs, in both unpartitioned and partitioned cases. As a result, partitioned and unpartitioned probe block graphs can be recognized in linear time.


Probe graph block graph probe block graph 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institut für InformatikUniversität RostockRostockGermany
  2. 2.Department of Computer Science and Information EngineeringNational Dong Hwa University, ShoufengHualienTaiwan

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