Fully Leafed Induced Subtrees

  • Alexandre Blondin Massé
  • Julien de Carufel
  • Alain Goupil
  • Mélodie Lapointe
  • Émile Nadeau
  • Élise VandommeEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10979)


We consider the problem \(\mathrm {LIS}\) of deciding whether there exists an induced subtree with exactly \(i \le n\) vertices and \(\ell \) leaves in a given graph G with n vertices. We study the associated optimization problem, that consists in computing the maximal number of leaves, denoted by \(L_G(i)\), realized by an induced subtree with i vertices, for \(0 \le i \le n\). We begin by proving that the \(\mathrm {LIS}\) problem is NP-complete in general. Then, we describe a nontrivial branch and bound algorithm that computes the function \(L_G\) for any simple graph G. In the special case where G is a tree of maximum degree \(\varDelta \), we provide a \(\mathcal {O}(n^3\varDelta )\) time and \(\mathcal {O}(n^2)\) space algorithm to compute the function \(L_G\).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Alexandre Blondin Massé
    • 1
  • Julien de Carufel
    • 2
  • Alain Goupil
    • 2
  • Mélodie Lapointe
    • 1
  • Émile Nadeau
    • 1
  • Élise Vandomme
    • 1
    Email author
  1. 1.Laboratoire de Combinatoire et d’Informatique MathématiqueUniversité du Québec à MontréalMontrealCanada
  2. 2.Laboratoire Interdisciplinaire de Recherche en Imagerie et en CombinatoireUniversité du Québec à Trois-RivièresTrois-RivièresCanada

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