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 stric...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.展开更多
基金Supported by the National Natural Science Foundation of China(No.11201409,No.11371327)the Natural Science Foundation of Hebei Province of China(No.A2013203009)
文摘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.
