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Connected Dominating Sets in Triangulations

Authors Prosenjit Bose , Vida Dujmović , Hussein Houdrouge , Pat Morin , Saeed Odak

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LIPIcs.ICALP.2026.41.pdf
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ACM Subject Classification
  • Human-centered computing → Graph drawings
  • Theory of computation → Computational geometry
  • Mathematics of computing → Graph algorithms
Keywords
  • connected domination
  • triangulations
  • planar graphs
  • graph drawing
  • collinear sets

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Abstract

A dominating set of a graph G is connected if it induces a connected graph in G. For planar triangulations, it has been known since 1990 that every n-vertex triangulation admits a connected dominating set of size at most n/2 - 1, and no improvement to this bound was known for over three decades. We break this longstanding barrier by showing that every n-vertex triangulation has a connected dominating set of size at most 10n/21. Equivalently, every triangulation admits a spanning tree with at least 11n/21 leaves. Moreover, we present an algorithm that computes such a set in optimal linear time. Our result narrows the gap to the best known lower bound and has graph drawing applications, establishing a bound for one-bend free sets and improving the known bound for simultaneous planar embeddings.

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Prosenjit Bose, Vida Dujmović, Hussein Houdrouge, Pat Morin, and Saeed Odak. Connected Dominating Sets in Triangulations. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 41:1-41:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.41

Author Details

Prosenjit Bose
  • School of Computer Science, Carleton University, Ottawa, Canada
Vida Dujmović
  • School of Computer Science and Electrical Engineering, University of Ottawa, Canada
Hussein Houdrouge
  • School of Computer Science, Carleton University, Ottawa, Canada
Pat Morin
  • School of Computer Science, Carleton University, Ottawa, Canada
Saeed Odak
  • Department of Computer Science, Aalto University, Espoo, Finland

Funding

  • Bose, Prosenjit: Research partially funded by NSERC.
  • Dujmović, Vida: Research partially funded by NSERC and a University of Ottawa Research Chair.
  • Houdrouge, Hussein: Research partially funded by NSERC.
  • Morin, Pat: Research partially funded by NSERC.

References

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