×

Median graphs: Characterizations, location theory and related structures. (English) Zbl 0931.05072

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.

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
PDFBibTeX XMLCite