Decomposition of Graphs into Paths - Botler, Fábio; Wakabayashi, Yoshiko (Anais do Concurso de Teses e Dissertações da SBC (CTD-SBC); 2017: Anais do XXX Concurso de Teses e Dissertações, 2017)
We study the Decomposition Conjecture posed by Barát and Thomassen (2006), which states that, for each 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 partition of its edge set into copies of T. In a series of papers, Thomassen has verified this conjecture for stars, some bistars, paths of length 3, and paths whose length is a power of 2. In this paper we prove this conjecture for paths of any given length. Our technique is then used to prove weakenings of a conjecture of Kouider and Lonc (1999), and a conjecture of Favaron, Genest and Kouider (2010), both for path decomposition of regular graphs.