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Bipartite Temporal Graphs and the Parameterized Complexity of Multistage 2-Coloring

Authors Till Fluschnik , Pascal Kunz

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Till Fluschnik
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
Pascal Kunz
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany

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Till Fluschnik and Pascal Kunz. Bipartite Temporal Graphs and the Parameterized Complexity of Multistage 2-Coloring. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 16:1-16:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


We consider the algorithmic complexity of recognizing bipartite temporal graphs. Rather than defining these graphs solely by their underlying graph or individual layers, we define a bipartite temporal graph as one in which every layer can be 2-colored in a way that results in few changes between any two consecutive layers. This approach follows the framework of multistage problems that has received a growing amount of attention in recent years. We investigate the complexity of recognizing these graphs. We show that this problem is NP-hard even if there are only two layers or if only one change is allowed between consecutive layers. We consider the parameterized complexity of the problem with respect to several structural graph parameters, which we transfer from the static to the temporal setting in three different ways. Finally, we consider a version of the problem in which we only restrict the total number of changes throughout the lifetime of the graph. We show that this variant is fixed-parameter tractable with respect to the number of changes.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Dynamic graph algorithms
  • structural parameters
  • NP-hardness
  • parameterized algorithms
  • multistage problems


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