graphs – Min path cover problem in Cormen et.al. question about notation

In the book on algorithms by Cormen et.al, the problem 26-2 describes how to obtain a min-path cover for a DAG via max-flow. I have a question about the notation. First, let me quote the problem here:


A path cover of a directed graph $G = (V, E)$ is a set $P$ of vertex-disjoint paths such that every vertex in $V$ is included in exactly one path in $P$. Paths may start and end anywhere, and they may be of any length, including $0$. A minimum path cover of $G$ is a path cover containing the fewest possible paths.

a. Give an efficient algorithm to find a minimum path cover of a directed acyclic graph $G =(V, E)$ (Hint: Assuming that $V = {1, 2, … , n}$, construct the graph $G’ = (V’,E’)$, where:

$$V’ = {x_0,x_1,dots x_n} cup {y_0, y_1, dots y_n} $$
$$E’={(x_0,x_i):i in V} cup {(y_i,y_0) : i in V} cup {(x_i,y_i):(i,j) in E}$$
and run a maximum-flow algorithm.)


What are the $x_i$ and $y_i$ here? Am I missing something obvious?