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 …

A feasible family of paths in a connected graph G is a family that contains at least one path
between any pair of vertices in G. Any feasible path family defines a convexity on G. Well …

Let G be a finite, simple, and undirected graph and let S be a set of vertices of G. If no vertex
of G that does not belong to S has two neighbors in S, then S is P_3-convex. The P_3 …

The notion of transit function is introduced to present a unifying approach for results and
ideas on intervals, convexities and betweenness in graphs and posets. Prime examples of …

In this paper, we study the geodetic convexity of graphs, focusing on the problem of the
complexity of computing a minimum hull set of a graph in several graph classes. For any two …

Let G be a finite simple connected graph. A vertex v is a boundary vertex of G if there exists a
vertex u such that no neighbor of v is further away from u than v. We obtain a number of …

Let G be a finite simple graph. Let S⊆ V (G), its closed interval I [S] is the set of all vertices
lying on shortest paths between any pair of vertices of S. The set S is convex if I [S]= S. In this …

Convex Partitions of Graphs induced by Paths of Order Three CC Centeno1† S. Dantas2‡
MC Dourado1§ D. Rautenbach3¶ J. Page 1 Discrete Mathematics and Theoretical …

Generic submodularity ratio γ γ is a general measurement to characterize how close a
nonnegative monotone set function is to be submodular. In this paper, we make a systematic …

A walk W between two non-adjacent vertices in a graph G is called tolled if the first vertex of
W is among vertices from W adjacent only to the second vertex of W, and the last vertex of W …