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Listing Spanning Trees of Outerplanar Graphs by Pivot-Exchanges

Authors Nastaran Behrooznia, Torsten Mütze

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Trees
Keywords
  • Spanning tree
  • generation
  • edge exchange
  • Hamilton path
  • Gray code

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Abstract

We prove that the spanning trees of any outerplanar triangulation G can be listed so that any two consecutive spanning trees differ in an exchange of two edges that share an end vertex. For outerplanar graphs G with faces of arbitrary lengths (not necessarily 3) we establish a similar result, with the condition that the two exchanged edges share an end vertex or lie on a common face. These listings of spanning trees are obtained from a simple greedy algorithm that can be implemented efficiently, i.e., in time {O}(n log n) per generated spanning tree, where n is the number of vertices of G. Furthermore, the listings correspond to Hamilton paths on the 0/1-polytope that is obtained as the convex hull of the characteristic vectors of all spanning trees of G.

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Nastaran Behrooznia and Torsten Mütze. Listing Spanning Trees of Outerplanar Graphs by Pivot-Exchanges. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.16

Author Details

Nastaran Behrooznia
  • Department of Computer Science, University of Warwick, Coventry, UK
Torsten Mütze
  • Institut für Mathematik, Universität Kassel, Germany
  • Department of Theoretical Computer Science and Mathematical Logic, Charles University, Prague, Czech Republic

Funding

This work was supported by Czech Science Foundation grant GA 22-15272S. Both authors participated in the workshop "Combinatorics, Algorithms and Geometry" in March 2024, which was funded by German Science Foundation grant 522790373.

Acknowledgements

We thank both reviewers of this paper for a number of very helpful suggestions that improved the writing.

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