License: 
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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2020.24
URN: urn:nbn:de:0030-drops-128909
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12890/
Bousquet, Nicolas ;
Ito, Takehiro ;
Kobayashi, Yusuke ;
Mizuta, Haruka ;
Ouvrard, Paul ;
Suzuki, Akira ;
Wasa, Kunihiro
Reconfiguration of Spanning Trees with Many or Few Leaves
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 [Takehiro Ito et al., 2011].
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.
BibTeX - Entry
@InProceedings{bousquet_et_al:LIPIcs:2020:12890,
author = {Nicolas Bousquet and Takehiro Ito and Yusuke Kobayashi and Haruka Mizuta and Paul Ouvrard and Akira Suzuki and Kunihiro Wasa},
title = {{Reconfiguration of Spanning Trees with Many or Few Leaves}},
booktitle = {28th Annual European Symposium on Algorithms (ESA 2020)},
pages = {24:1--24:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-162-7},
ISSN = {1868-8969},
year = {2020},
volume = {173},
editor = {Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12890},
URN = {urn:nbn:de:0030-drops-128909},
doi = {10.4230/LIPIcs.ESA.2020.24},
annote = {Keywords: combinatorial reconfiguration, spanning trees, PSPACE, polynomial-time algorithms}
}
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Keywords: |
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combinatorial reconfiguration, spanning trees, PSPACE, polynomial-time algorithms |
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Collection: |
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28th Annual European Symposium on Algorithms (ESA 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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26.08.2020 |
