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Connected Partitions via Connected Dominating Sets

Authors Aikaterini Niklanovits , Kirill Simonov , Shaily Verma , Ziena Zeif

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  • Theory of computation → Graph algorithms analysis
Keywords
  • Győri-Lovász theorem
  • connected dominating sets
  • graph classes

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Abstract

The classical theorem due to Győri and Lovász states that any k-connected graph G admits a partition into k connected subgraphs, where each subgraph has a prescribed size and contains a prescribed vertex, as long as the total size of target subgraphs is equal to the size of G. However, this result is notoriously evasive in terms of efficient constructions, and it is still unknown whether such a partition can be computed in polynomial time, even for k = 5.
We make progress towards an efficient constructive version of the Győri-Lovász theorem by considering a natural strengthening of the k-connectivity requirement. Specifically, we show that the desired connected partition can be found in polynomial time, if G contains k disjoint connected dominating sets. As a consequence of this result, we give several efficient approximate and exact constructive versions of the original Győri-Lovász theorem:  
- On general graphs, a Győri-Lovász partition with k parts can be computed in polynomial time when the input graph has connectivity Ω(k ⋅ log² n); 
- On convex bipartite graphs, connectivity of 4k is sufficient; 
- On biconvex graphs and interval graphs, connectivity of k is sufficient, meaning that our algorithm gives a "true" constructive version of the theorem on these graph classes.

Cite As Get BibTex

Aikaterini Niklanovits, Kirill Simonov, Shaily Verma, and Ziena Zeif. Connected Partitions via Connected Dominating Sets. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.10

Author Details

Aikaterini Niklanovits
  • Hasso Plattner Institute, University of Potsdam, Germany
Kirill Simonov
  • Department of Informatics, University of Bergen, Norway
Shaily Verma
  • Hasso Plattner Institute, University of Potsdam, Germany
Ziena Zeif
  • Hasso Plattner Institute, University of Potsdam, Germany

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