Circumferences of regular claw-free graphs Original Research Article

A known result obtained independently by Fan and Jung is that every 3-connected k-regular graph on n vertices contains a cycle of length at least image. This raises the question of how much can be said about the circumferences of 3-connected k-regular claw-free graphs. In this paper, we show that every 3-connected k-regular claw-free graph on n vertices contains a cycle of length at least image.