  Let $G$ be a graph with chordal complement and $I(G)$ its edge ideal. From
work of Herzog, Hibi, and Zheng, it is known that $I(G)$ has linear quotients
and all of its powers have linear resolutions. For edge ideals $I(G)$ arising
from graphs which do not have chordal complements, exact conditions on their
powers possessing linear resolutions or linear quotients are harder to find. We
provide here an explicit linear quotients ordering for all powers of the edge
ideal of the antipath and a linear quotients ordering on the second power of
$I(A_n)^2$ of the edge ideal of the anticycle $A_n$. This linear quotients
ordering on $I(A_n)$ recovers a prior result of Nevo that $I(A_n)^2$ has a
linear resolution.
