## Abstract

Barát and Thomassen have conjectured that, for any fixed tree *T*, there exists a natural number *k*
_{
T
} such that the following holds: If *G* is a *k*
_{
T
}-edge-connected graph such that |*E*(*T*)| divides |*E*(*G*)|, then *G* has a *T*-decomposition. The conjecture is trivial when *T* has one or two edges. Before submission of this paper, the conjecture had been verified only for two other trees: the paths of length 3 and 4, respectively. In this paper we verify the conjecture for each path whose length is a power of 2.

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Thomassen, C. Decomposing graphs into paths of fixed length.
*Combinatorica* **33, **97–123 (2013). https://doi.org/10.1007/s00493-013-2633-7

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### Mathematics Subject Classification (2000)

- 05C38
- 05C40