The induced path convexity, betweenness, and svelte graphs Original Research Article

The induced path interval J(u,v) consists of the vertices on the induced paths between u and v in a connected graph G. Differences in properties with the geodesic interval are studied. Those graphs are characterized, in which the induced path intervals define a proper betweenness. The intersection of the induced path intervals between the pairs of a triple, in general, consists of a big chunk of vertices. The graphs, in which this intersection consists of at most one vertex, for each triple of vertices, are characterized by forbidden subgraphs.