Schmeichel and Hakimi ?], and Bauer and Schmeichel ?] gave an evidence in support of the well-known Bondy's "metaconjecture" that almost any non-trivial condition on graphs which implies that the graph is hamiltonian also implies that it is pancyclic. In particular, they proved that the metaconjecture is valid for Chvv atal's condition ?]. We slightly generalize their results giving a new Chvv ...

The super line graph of index r of a graph G has the r-sets of edges as its vertices, with two being adjacent if one has an edge that is adjacent to an edge in the other. In this paper, we continue our investigation of this graph by establishing two results, the first on the independence number of super line graphs of arbitrary index and the second on pancyclicity in the index-2 case.

We call a graph G pancyclic if it contains at least one cycle of every possible length m, for 3 ≤ m ≤ |V (G)|. In this paper, we define a new property called chorded pancyclicity. We explore forbidden subgraphs in claw-free graphs sufficient to imply that the graph contains at least one chorded cycle of every possible length 4, 5, . . . , |V (G)|. In particular, certain paths and triangles with...