P1 & P2 Path Partition: Same End Vertices Possible?

[kimkibun]

sorry if i posted this topic here..let P₁ and P₂ be a path partition of a graph.is it possible that P₁ and P₂ to have the same end vertices?

 

[MathematicalPhysicist]

Yes, for example a some cycle.

 

[kimkibun]

but sir, according to the definition of path partition, it should be vertex-disjoint..