General results on tolerance intersection graphs
Michael S. Jacobson, Fred R. McMorris, Edward R. Scheinerman · Journal of Graph Theory · 1991
Abstract In this paper, general results are presented that are related to ϕ‐tolerance intersection graphs previously defined by Jacobson, McMorris, and Mulder. For example, it is shown that all graphs are ϕ‐tolerance intersection graphs for all ϕ, yet for “nice” ϕ, almost no graphs are ϕ‐tolerance interval graphs. Additional results about representation of trees are given.