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Reconfiguration of Spanning Trees with Degree Constraint or Diameter Constraint

Authors Nicolas Bousquet , Takehiro Ito , Yusuke Kobayashi , Haruka Mizuta, Paul Ouvrard, Akira Suzuki , Kunihiro Wasa

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Author Details

Nicolas Bousquet
  • CNRS, LIRIS, Université de Lyon, France
Takehiro Ito
  • Graduate School of Information Sciences, Tohoku University, Japan
Yusuke Kobayashi
  • Research Institute for Mathematical Sciences, Kyoto University, Japan
Haruka Mizuta
  • Graduate School of Information Sciences, Tohoku University, Japan
Paul Ouvrard
  • Université de Bordeaux, France
Akira Suzuki
  • Graduate School of Information Sciences, Tohoku University, Japan
Kunihiro Wasa
  • Toyohashi University of Technology, Japan

Funding

This work is partially supported by JSPS and MEAE-MESRI under the Japan-France Integrated Action Program (SAKURA).
  • Bousquet, Nicolas: This work was supported by ANR project GrR (ANR-18-CE40-0032).
  • Ito, Takehiro: Partially supported by JSPS KAKENHI Grant Numbers JP18H04091, JP19K11814 and JP20H05793, Japan.
  • Kobayashi, Yusuke: Partially supported by JSPS KAKENHI Grant Numbers 18H05291, JP20K11692, and 20H05795, Japan.
  • Ouvrard, Paul: This work was supported by ANR project GrR (ANR-18-CE40-0032).
  • Suzuki, Akira: Partially supported by JSPS KAKENHI Grant Numbers JP18H04091, JP20K11666 and JP20H05794, Japan.
  • Wasa, Kunihiro: Partially supported by JST CREST Grant Numbers JPMJCR18K3 and JPMJCR1401, and JSPS KAKENHI Grant Numbers 19K20350 and JP20H05793, Japan.

Acknowledgements

The authors thank anonymous reviewers for their valuable comments.

Cite AsGet BibTex

Nicolas Bousquet, Takehiro Ito, Yusuke Kobayashi, Haruka Mizuta, Paul Ouvrard, Akira Suzuki, and Kunihiro Wasa. Reconfiguration of Spanning Trees with Degree Constraint or Diameter Constraint. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 15:1-15:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.STACS.2022.15

Abstract

We investigate the complexity of finding a transformation from a given spanning tree in a graph to another given spanning tree in the same graph via a sequence of edge flips. The exchange property of the matroid bases immediately yields that such a transformation always exists if we have no constraints on spanning trees. In this paper, we wish to find a transformation which passes through only spanning trees satisfying some constraint. Our focus is bounding either the maximum degree or the diameter of spanning trees, and we give the following results. The problem with a lower bound on maximum degree is solvable in polynomial time, while the problem with an upper bound on maximum degree is PSPACE-complete. The problem with a lower bound on diameter is NP-hard, while the problem with an upper bound on diameter is solvable in polynomial time.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • combinatorial reconfiguration
  • spanning trees
  • PSPACE
  • polynomial-time algorithms

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