Degree sums and subpancyclicity in line graphs Original Research Article

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, we show 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. Our results shed some light on the content of a famous Metaconjecture of Bondy.