Reconfiguration of spanning trees with many or few leaves

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

研究成果: Conference contribution

抄録

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.

本文言語English
ホスト出版物のタイトル28th Annual European Symposium on Algorithms, ESA 2020
編集者Fabrizio Grandoni, Grzegorz Herman, Peter Sanders
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN(電子版)9783959771627
DOI
出版ステータスPublished - 2020 8 1
イベント28th Annual European Symposium on Algorithms, ESA 2020 - Virtual, Pisa, Italy
継続期間: 2020 9 72020 9 9

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
173
ISSN(印刷版)1868-8969

Conference

Conference28th Annual European Symposium on Algorithms, ESA 2020
国/地域Italy
CityVirtual, Pisa
Period20/9/720/9/9

ASJC Scopus subject areas

  • ソフトウェア

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