A Chvátal–Erdős type condition for pancyclability Original Research Article

Let image be a graph and image a subset of image. Let image denote the maximum number of pairwise nonadjacent vertices in the subgraph image of image induced by image. If image is not complete, let image denote the smallest number of vertices separating two vertices of image and image otherwise. We prove that if image and image is large enough (depending on image), then image is image-pancyclable, that is contains cycles with exactly image vertices of image for every image, image.