CPL - Chalmers Publication Library

A variant of the discrete isoperimetric problem

Peter Hegarty (Institutionen för matematik)
Ars Combin. Vol. 73 (2004), p. 263--274.

We consider a variant of what is known as the discrete isoperimetric problem, namely the problem of minimising the size of the boundary of a family of subsets of a finite set. We use the technique of \$\lq\$shifting' to provide an alternative proof of a result of Hart. This technique was introduced in the early 1980s by Frankl and F\"{u}redi and gave alternative proofs of previously known classical results like the discrete isoperimetric problem itself and the Kruskal-Katona theorem. Hence our purpose is to bring Hart's result into this general framework.