Graphs and finite distributive partial lattices
Median graphs constitute a well-known and widely studied class of graphs; see for example the papers [\textit{H. J. Bandelt} and \textit{J. Hedlikova}, Discrete Math. 45, 1-30 (1983; Zbl 0506.06005)] and \textit{H. J. Bandelt} and \textit{H. M. Mulder}, J. Graph Theory 7, 487-497 (1983; Zbl 0525.05055)] and the references therein. They constitute a subclass of the Hasse diagram graphs of distributive partial lattices. In this paper we give a characterization for the Hasse diagram graphs G of finite distributive partial lattices by means of prime convexes of G. This characterization generalizes that of Mulder and Schrijver for median graphs reprinted in [the first cited paper, Theorem 2.2].
scientific article; zbMATH DE number 4106908