This monograph is intended to present the current state of the art of the so-called theory of
geodesic convexity in finite, simple, connected graphs. It has been designed with the …

We systematically study the query complexity of learning geodesically convex halfspaces on
graphs. Geodesic convexity is a natural generalisation of Euclidean convexity and allows …

We prove that the combinatorial optimization problem of determining the hull number of a
partial cube is NP-complete. This makes partial cubes the minimal graph class for which NP …

The general position problem in graph theory asks for the largest set S of vertices of a graph
G such that no shortest path of G contains more than two vertices of S. In this paper we …

In this paper, we study two graph convexity parameters: iteration time and general position
number. The iteration time was defined in 1981 in the geodesic convexity, but its …

Partially answering a question posed by Araujo, Morel, Sampaio, Soares, and Weber, we
show that computing the geodetic hull number of a given P 9-free graph is NP-hard …

In this paper, we introduce a new convexity on graphs similar to the well known P 3-
convexity, which we will call P 3∗-convexity. We show that several P 3∗-convexity …

Given a graph G and a pair of vertices u, v the interval IG [u, v] is the set of all vertices that
are in some shortest path between u and v. Given a subset X of vertices of G, the interval IG …

In a triangle path v 1,…, vt of a graph G no edges exist joining vertices vi and vj such that| j−
i|> 2. A set S⊆ V (G) is convex in the triangle path convexity of G, or t-convex, if the vertices …

In the geodetic convexity, a set of vertices S of a graph G is convex if all vertices belonging to
any shortest path between two vertices of S lie in S. The convex hull H (S) of S is the …