, Volume 64, Issue 1, pp 85–111 | Cite as

Parameterized Complexity of the Spanning Tree Congestion Problem

  • Hans L. Bodlaender
  • Fedor V. Fomin
  • Petr A. Golovach
  • Yota Otachi
  • Erik Jan van Leeuwen
Open Access


We study the problem of determining the spanning tree congestion of a graph. We present some sharp contrasts in the parameterized complexity of this problem. First, we show that on apex-minor-free graphs, a general class of graphs containing planar graphs, graphs of bounded treewidth, and graphs of bounded genus, the problem to determine whether a given graph has spanning tree congestion at most k can be solved in linear time for every fixed k. We also show that for every fixed k and d the problem is solvable in linear time for graphs of degree at most d. In contrast, if we allow only one vertex of unbounded degree, the problem immediately becomes NP-complete for any fixed k≥8. Moreover, the hardness result holds for graphs excluding the complete graph on 6 vertices as a minor. We also observe that for k≤3 the problem becomes polynomially time solvable.


Spanning tree congestion Graph minor Parameterized algorithms Apex graph 


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Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  • Fedor V. Fomin
    • 2
  • Petr A. Golovach
    • 3
  • Yota Otachi
    • 4
  • Erik Jan van Leeuwen
    • 2
  1. 1.Department of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  2. 2.Department of InformaticsUniversity of BergenBergenNorway
  3. 3.School of Engineering and Computing SciencesDurham UniversityDurhamUK
  4. 4.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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