Have You Ever Meta-Conjectured?

The study of cycles has a long and varied history. In 1971, Bondy noted a tie linking hamiltonian graphs and pancyclic graphs. He stated his famed meta-conjecture: Almost any nontrivial condition on a graph which implies that the graph is Hamiltonian also implies that the graph is pancyclic. There may be some simple family of exceptional graphs. A cycle is said to be chorded if there exists an edge between two vertices of the cycle that is not an edge of the cycle. A cycle is said to be chorded if it induces at least one chord. In this talk I will extend Bondy’s meta-conjecture in several ways to a broader class of cycle problems in graphs, namely to finding conditons that imply the existence of various types of chorded cycles. I will offer supporting results to each new meta-conjecture.

Keywords: meta-conjecture, pancyclic, chorded cycle