Reconfiguration of Spanning Trees with Degree Constraints or Diameter Constraints

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 constrai...

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Bibliographic Details
Published in:Algorithmica Vol. 85; no. 9; pp. 2779 - 2816
Main Authors: Bousquet, Nicolas, Ito, Takehiro, Kobayashi, Yusuke, Mizuta, Haruka, Ouvrard, Paul, Suzuki, Akira, Wasa, Kunihiro
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2023
Springer Nature B.V
Springer Verlag
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Graph theory
Lower bounds
Mathematics of Computing
Polynomials
Reconfiguration
Theory of Computation
Transformations
Upper bounds
Combinatorial reconfiguration
Polynomial-time algorithms
PSPACE
Spanning trees
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary: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.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-023-01117-z