The sparse random-graph path decomposition conjecture

Let $G\sim G_{n,p}$, where $p=o(1)$ and $pn/\log n\to\infty$, and let $odd(G)$ denote the number of odd-degree vertices of $G$. Sparse random-graph path decomposition conjecture. Asymptotically almost surely, $G$ can be decomposed into $odd(G)/2$ paths. This would extend the paper's exact path-decomposition result for constant edge probability into a sparse regime; the stated range is left as a belief in the source and is not proved there.