On Strong Tree-Breadth

  • Arne LeitertEmail author
  • Feodor F. Dragan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10043)


In this paper, we introduce and investigate a new notion of strong tree-breadth. We say that a graph G has strong tree-breadth \(\rho \) if there is a tree-decomposition T for G such that each bag B of T is equal to the complete \(\rho \)-neighbourhood of some vertex v in G, i. e., \(B = N_G^\rho [v]\). We show that
  • it is NP-complete to determine if a given graph has strong tree-breadth \(\rho \), even for \(\rho = 1\);

  • if a graph G has strong tree-breadth \(\rho \), then we can find a tree-decomposition for G with tree-breadth \(\rho \) in \(\mathcal {O}(n^2m)\) time;

  • with some additional restrictions, a tree-decomposition with strong breadth \(\rho \) can be found in polynomial time;

  • some graph classes including distance-hereditary graphs have strong tree-breadth 1.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceKent State UniversityKentUSA

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