A graph G is called k-neighborhood chordal if for every vertex set A, such that IAl 6 k and G(A) connected, the graph UvEA G(Tv) is chordal. A family of subtrees of a graph is called k-acyclic if the union of any k subtrees is acyclic. A graph is l-neighborhood chordal iff it is an intersection graph of a Helly 2-acyclic family of subtrees (Gavril, 1987… (More)