On the Helly property working as a compactness criterion on graphs
Given a connected graph (X,E), denote by \(d_ G\) the distance given by the graph. Let \({\mathcal E}\) be a family of all balls, i.e. sets \(\{\) \(y\in X;d_ G(x,y)\leq p\}\), \(x\in X\), \(p\in N\). Then (X,E) is a Helly graph provided every subfamily of \({\mathcal E}\) in which every pair of balls meets has a non-trivial intersection. The automorphism group of a finite Helly graph is studied and fixed point theorem for finite Helly graphs is proved.
scientific article; zbMATH DE number 3918391
scientific article