On supercompact graphs
Chong‐Keang Lim · Journal of Graph Theory · 1978
Abstract A graph G is called a supercompact graph if G is the intersection graph of some family 𝒯 of subsets of a set X such that 𝒯 satisfies the Helly property and for any x≠y in X, there exists S ∈ 𝒯 with x ∈ S, y ∉ S. Various characterizations of supercompact graphs are given. It is shown that every clique‐critical graph is supercompact. Furthermore, for any finite graph, H, there is at most a finite number of different supercompact graphs G such that H is the clique‐graph of G.