On the Connected Spanning Cubic Subgraph Problem

  • Damien Massé
  • Reinhardt Euler
  • Laurent Lemarchand
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 148)


Given an \(n \times n\)-distance matrix D, the connected spanning cubic subgraph problem (\(\mathcal {CSC}\)) is to determine a connected cubic graph \(G=(V,E)\) of order n with total distance \(\sum _{ij \in E} d_{ij}\) as small as possible. Restricting matrix D to have 0–1 entries only leads to the problem of deciding whether a given graph contains a connected spanning cubic subgraph. We present some first results on the facial structure of the associated polytope including several classes of valid inequalities some of which are shown to be facet-defining. To solve problem \(\mathcal {CSC}\), two procedures are formulated: the first is based on a binary linear program, that iteratively constructs an optimal solution, the second on a linear program, that iteratively exploits additional cutting planes from different families to accelerate the solution process. All formulations have been implemented and tested on series of randomly generated problem instances.


Connected spanning cubic subgraph 0–1 polytope 0–1 programming Branch and Cut 

AMS Subject Classification:

90C27 90C35 90C57 05C99 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Damien Massé
    • 1
  • Reinhardt Euler
    • 1
  • Laurent Lemarchand
    • 1
  1. 1.Lab-STICC UMR 6285UBO-Université Européenne de BretagneBrestFrance

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