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arXiv · 1505.04309

Decompositions of highly connected graphs into paths of length five

Fábio Botler·Guilherme O. Mota·Marcio T. I. Oshiro·Yoshiko Wakabayashi
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Abstract

We study the Decomposition Conjecture posed by Barát and Thomassen (2006), which states that for every tree $T$ there exists a natural number $k_T$ such that, if $G$ is a $k_T$-edge-connected graph and $|E(T)|$ divides $|E(G)|$, then $G$ admits a decomposition into copies of $T$. In a series of papers, Thomassen verified this conjecture for stars, some bistars, paths of length $3$, and paths whose length is a power of $2$. We verify the Decomposition Conjecture for paths of length $5$.

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Fábio Botler, Guilherme O. Mota, Marcio T. I. Oshiro, Yoshiko Wakabayashi. 2015-07-28. Decompositions of highly connected graphs into paths of length five. https://arxiv.org/abs/1505.04309

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