Walking the Approximate Longest Path

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    I couldn't understand the sentence in Editorial.

    Let's choose arbitrary permutation p and add orientation for all edges of G with respect of p i.e. if (x,y) belongs to E and p^-1(x) < p^-1(y) then edge is directed like x -> y.

    If I could find an arbitrary permutation that fits in a ucg like the problem statement, wouldn't this permutation be the longest path?

    What does it mean by p^-1(x) < p^-1(y) ?