Degree sums and subpancyclicity in line graphs (Q5957759)

A graph is called subpancyclic if it contains a cycle of length \(k\) for each \(k\) between 3 and the circumference of the graph. In this paper, it is shown that if the degree sum of the vertices along each 2-path of a graph \(G\) exceeds \((n+6)/2\), or if the degree sum of the vertices along each 3-path of \(G\) exceeds \((2n+16)/3\), then its line graph \(L(G)\) is subpancyclic. Simple examples show that these bounds are best possible.