Intersection theorems for infinite families of convex sets in graphs (Q1276308)

A Helly-type theorem determines the least cardinal \(n\) such that any family of ``convex'' sets in some infinite graph has a nonempty intersection whenever each of its subfamilies of cardinality less than \(n\) has a nonempty intersection. The author studies geodesic convexity. Most of his results ``remain valid if we replace the geodesic convexity by any graph convexity, and in particular, by minimal path convexity''.