Reconfiguration of spanning trees with many or few leaves

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Let G be a graph and T1,T2 be two spanning trees of G. We say that T1 can be transformed into T2 via an edge flip if there exist two edges e ∈ T1 and f in T2 such that T2 = (T1 \e)∪f. Since spanning trees form a matroid, one can indeed transform a spanning tree into any other via a sequence of edge flips, as observed in [11]. We investigate the problem of determining, given two spanning trees T1,T2 with an additional property Π, if there exists an edge flip transformation from T1 to T2 keeping property Π all along. First we show that determining if there exists a transformation from T1 to T2 such that all the trees of the sequence have at most k (for any fixed k ≥ 3) leaves is PSPACE-complete. We then prove that determining if there exists a transformation from T1 to T2 such that all the trees of the sequence have at least k leaves (where k is part of the input) is PSPACE-complete even restricted to split, bipartite or planar graphs. We complete this result by showing that the problem becomes polynomial for cographs, interval graphs and when k = n-2.

Original languageEnglish
Title of host publication28th Annual European Symposium on Algorithms, ESA 2020
EditorsFabrizio Grandoni, Grzegorz Herman, Peter Sanders
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771627
DOIs
Publication statusPublished - 2020 Aug 1
Event28th Annual European Symposium on Algorithms, ESA 2020 - Virtual, Pisa, Italy
Duration: 2020 Sep 72020 Sep 9

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume173
ISSN (Print)1868-8969

Conference

Conference28th Annual European Symposium on Algorithms, ESA 2020
CountryItaly
CityVirtual, Pisa
Period20/9/720/9/9

Keywords

  • Combinatorial reconfiguration
  • PSPACE
  • Polynomial-time algorithms
  • Spanning trees

ASJC Scopus subject areas

  • Software

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