  A path partition (also referred to as a linear forest) of a graph $G$ is a
set of vertex-disjoint paths which together contain all the vertices of $G$. An
isolated vertex is considered to be a path in this case. The path partition
conjecture states that every $n$-vertices $d$-regular graph has a path
partition with at most $\frac{n}{d+1}$ paths. The conjecture has been proved
for all $d<6$. We prove the conjecture for $d=6$.
