Long cycles containing image-ordered vertices in graphs Original Research Article

Let G be a image-connected graph on n vertices and image be any ordered set of vertices, that is, the vertices in S appear in the order of the sequence image. We will show that if there exists a cycle containing image in the given order, then there exists a cycle C containing image in the given order such that image where image when G is not complete, otherwise set image. This generalizes several related results known before.