Relative length of longest paths and longest cycles in triangle-free graphs Original Research Article

In this paper, we study triangle-free graphs. Let image be an arbitrary triangle-free graph with minimum degree at least two and image. We first show that either for any path image in image there exists a cycle image such that image, or image is isomorphic to exactly one exception. Using this result, we show that for any set image of at most image vertices in image there is a cycle image such that image.