A note on G-intersecting families

  title={A note on G-intersecting families},
  author={Tom Bohman and Ryan R. Martin},
  journal={Discrete Mathematics},
Consider a graph G and a k-uniform hypergraph H on common vertex set [n]. We say that H is G-intersecting if for every pair of edges in X; Y ∈H there are vertices x∈X and y∈ Y such that x=y or x and y are joined by an edge in G. This notion was introduced by Bohman, Frieze, Ruszink6 o and Thoma who proved a natural generalization of the Erdős–Ko–Rado Theorem for G-intersecting k-uniform hypergraphs for G sparse and k =O(n). In this note, we extend this result to k = O( √ n). c © 2002 Elsevier… CONTINUE READING