On an equivalence in discrete extremal problems

We introduce some equivalence relations on graphs and posets and prove that they are closed under the cartesian product operation. These relations concern the edge-isoperimetric problem on graphs and the shadow minimization problems on posets. For a long time these problems have been considered quite independently. We present close connections between them. In particular we show that a number of known results concerning the edge-isoperimetric problem for concrete families of graphs are direct consequences of the Macauleyness of appropriate posets.

• Type: Journal
• Year: 1999
• Where: DM
• Authors: Sergei L. Bezrukov
• Keywords: Cartesian Product Operation, DM 1999, Edge-isoperimetric Problem, Shadow Minimization Problems