Given a graph G, let Q(G) denote the collection of all independent
(edge-free) sets of vertices in G. We consider the problem of determining the
size of a largest antichain in Q(G).
  When G is the edge-less graph, this problem is resolved by Sperner's Theorem.
In this paper, we focus on the case where G is the path of length n-1, proving
the size of a maximal antichain is of the same order as the size of a largest
layer of Q(G).Comment: 26 page