Separation Dimension of Graphs and Hypergraphs

Separation dimension of a hypergraph H, denoted by $\mathit{\pi }(H)$ , is the smallest natural number k so that the vertices of H can be embedded in ${‐{R}}^k$ such that any two disjoint edges of H can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph H is equal to the boxicity of the line graph of H. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension. In this paper, we study the separation dimension of hypergraphs and graphs.