Non-separating 2-factors of an even-regular graph Original Research Article

For a 2-factor image of a connected graph image, we consider image, which is the graph obtained from image by removing all the edges of image. If image is connected, image is said to be a non-separating 2-factor. In this paper we study a sufficient condition for a image-regular connected graph image to have such a 2-factor. As a result, we show that a image-regular connected graph image has a non-separating 2-factor whenever the number of vertices of image does not exceed image.