Median Graphs: Characterizations, Location Theory and Related Structures

Median graphs are surveyed from the point of view of their characterizations, their role in location theory, and their connections with median structures. The median structures we present include ternary algebras, betweenness, interval structures, semilattices, hypergraphs, join geometries, and conflict models. In addition, some new characterizations of median graphs as meshed graphs are presented and a new characterization in terms of location theory is given.