We extend known results on chordal graphs and distance-hereditary graphs to much larger
graph classes by using only a common metric property of these graphs. Specifically, a graph …

A graph is Helly if every family of pairwise intersecting balls has a nonempty common
intersection. The class of Helly graphs is the discrete analogue of the class of hyperconvex …

Abstract A graph G=(V, E) is distance hereditary if every induced path of G is a shortest path.
In this paper, we show that the eccentricity function e (v)= max⁡{d (v, u): u∈ V} in any …

A new metric parameter for a graph, Helly-gap, is introduced. A graph G is called α-weakly-
Helly if any system of pairwise intersecting disks in G has a nonempty common intersection …

The δ-hyperbolicity of a graph can be viewed as a measure of how close a graph is to a tree
metrically; the smaller the hyperbolicity of a graph, the closer it is metrically to a tree. For …