Klavžar, Sandi; Mulder, Henry Martyn Median graphs: Characterizations, location theory and related structures. (English) Zbl 0931.05072 J. Comb. Math. Comb. Comput. 30, 103-127 (1999). Summary: Median graphs are surveyed from the point of view of their characterizations, their role in location theory and their connection 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 is given. Cited in 1 ReviewCited in 65 Documents MSC: 05C75 Structural characterization of families of graphs 05C12 Distance in graphs 05C99 Graph theory 05C65 Hypergraphs 06A12 Semilattices 08A99 Algebraic structures 52A35 Helly-type theorems and geometric transversal theory 52A99 General convexity 90B80 Discrete location and assignment Keywords:location theory; median structures; ternary algebras; betweenness; interval structures; semilattices; hypergraphs; join geometries; meshed graphs; characterization PDFBibTeX XMLCite \textit{S. Klavžar} and \textit{H. M. Mulder}, J. Comb. Math. Comb. Comput. 30, 103--127 (1999; Zbl 0931.05072)