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Trade-Off Between Spread and Width for Tree Decompositions

Authors Hans L. Bodlaender , Carla Groenland

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LIPIcs.WG.2026.9.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Trees
  • Theory of computation → Fixed parameter tractability
Keywords
  • Tree decomposition
  • spread
  • domino treewidth

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Abstract

We study the trade-off between (average) spread and width in tree decompositions, answering several questions from Wood [arXiv:2509.01140]. The spread of a vertex v in a tree decomposition is the number of bags that contain v. Wood asked for which c > 0, there exists c' such that each graph G has a tree decomposition of width ctw(G) in which each vertex v has spread at most c'(d(v)+1). We show that c ≥ 2 is necessary and that c > 3 is sufficient. Moreover, we answer a second question fully by showing that near-optimal average spread can be achieved simultaneously with width O(tw(G)).

Cite As Get BibTex

Hans L. Bodlaender and Carla Groenland. Trade-Off Between Spread and Width for Tree Decompositions. In 52nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 376, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.WG.2026.9

Author Details

Hans L. Bodlaender
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Carla Groenland
  • Faculty of Electrical Engineering, Mathematics and Computer Science, Technical University Delft, The Netherlands

Funding

  • Groenland, Carla: Research supported by the Dutch Research Council (NWO, VI.Veni. 232.073).

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