Subpancyclicity of line graphs and degree sums along paths Original Research Article

A graph is called subpancyclic if it contains a cycle of length image for each image between 3 and the circumference of the graph. We show that if image is a connected graph on image vertices such that image for all four vertices image of any path image in image, then the line graph image is subpancyclic, unless image is isomorphic to an exceptional graph. Moreover, we show that this result is best possible, even under the assumption that image is hamiltonian. This improves earlier sufficient conditions by a multiplicative factor rather than an additive constant.