Decomposition of $(2k+1)$-regular graphs containing special spanning $2k$-regular Cayley graphs into paths of length $2k+1$

Fábio Botler, Luiz Hoffmann

A $P_{\ell }$-decomposition of a graph $G$ is a set of paths with $\ell$ edges in $G$ that cover the edge set of $G$. Favaron, Genest, and Kouider (2010) conjectured that every $(2k+1…