For a graph G and an integer r≥1,G is r-EKR if no intersecting family of independent r-sets of G is larger than the largest star(a family of independent r-sets containing some fixed vertex in G),and G is strictly r-EKR if every extremal intersecting family of independent r-sets is a star.Recently,Hurlbert and Kamat gave a preliminary result about EKR property of ladder graphs.They showed that a ladder graph with n rungs is 3-EKR for all n≥3.The present paper proves that this graph is r-EKR for all 1≤r≤n,and strictly r-EKR except for r=n-1.
