Helly property in finite set systems
This paper investigates the combinatorial counterparts of the famous Helly theorem: a finite set system satisfies the \(d\)-dimensional Helly property if every subsystem with empty intersection has a sub-subsystem of at most \(d+1\) elements with an empty intersection, again. Numerous extremal properties of \(d\)-dimensional Helly systems are proven including LYM-type inequalities. The results generalize several former theorems of B. Bollobás and P. Duchet. More open problems are formulated including a ``full'' LYM-type inequality.
scientific article; zbMATH DE number 165747
scientific article