Boxicity and Separation Dimension
نویسندگان
چکیده
A family F of permutations of the vertices of a hypergraph H is called pairwise suitable for H if, for every pair of disjoint edges in H , there exists a permutation in F in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for H is called the separation dimension of H and is denoted by π(H). Equivalently, π(H) is the smallest natural number k so that the vertices of H can be embedded in R 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.
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