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- W3082258454 abstract "Let $G$ be a graph and $T_1,T_2$ be two spanning trees of $G$. We say that $T_1$ can be transformed into $T_2$ via an edge flip if there exist two edges $e in T_1$ and $f$ in $T_2$ such that $T_2= (T_1 setminus e) cup f$. Since spanning trees form a matroid, one can indeed transform a spanning tree into any other via a sequence of edge flips, as observed by Ito et al. We investigate the problem of determining, given two spanning trees $T_1,T_2$ with an additional property $Pi$, if there exists an edge flip transformation from $T_1$ to $T_2$ keeping property $Pi$ all along. First we show that determining if there exists a transformation from $T_1$ to $T_2$ such that all the trees of the sequence have at most $k$ (for any fixed $k ge 3$) leaves is PSPACE-complete. We then prove that determining if there exists a transformation from $T_1$ to $T_2$ 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 $k=n-2$." @default.
- W3082258454 created "2020-09-08" @default.
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- W3082258454 date "2020-06-25" @default.
- W3082258454 modified "2023-09-23" @default.
- W3082258454 title "Reconfiguration of Spanning Trees with Many or Few Leaves" @default.
- W3082258454 hasPublicationYear "2020" @default.
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