On spanning connected graphs

A k-container image of G between image and image is a set of k internally disjoint paths between image and image. A k-container image of G is a image-container if the set of the vertices of all the paths in image contains all the vertices of G. A graph G is image-connected if there exists a image-container between any two distinct vertices. Therefore, a graph is image-connected (respectively, image-connected) if and only if it is hamiltonian connected (respectively, hamiltonian). In this paper, a classical theorem of Ore, providing sufficient conditional for a graph to be hamiltonian (respectively, hamiltonian connected), is generalized to image-connected graphs.