Mixed-Integer Programming Techniques for the Connected Max-k-Cut Problem

Christopher Hojny (Corresponding author), Imke Joormann, Hendrik Lüthen, Martin Schmidt

Research output: Contribution to journalArticleAcademicpeer-review

12 Citations (Scopus)


We consider an extended version of the classical Max-k-Cut problem in which we additionally require that the parts of the graph partition are connected. For this problem we study two alternative mixed-integer linear formulations and review existing as well as develop new branch-and-cut techniques like cuts, branching rules, propagation, primal heuristics, and symmetry breaking. The main focus of this paper is an extensive numerical study in which we analyze the impact of the different techniques for various test sets. It turns out that the techniques from the existing literature are not sufficient to solve an adequate fraction of the test sets. However, our novel techniques significantly outperform the existing ones both in terms of running times and the overall number of instances that can be solved.

Original languageEnglish
Pages (from-to)75-132
Number of pages58
JournalMathematical Programming Computation
Early online date30 Apr 2020
Publication statusPublished - Mar 2021


  • Branch-and-cut
  • Connectivity
  • Max-cut
  • Mixed-integer programming


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