Pancyclicity when each cycle must pass exactly $k$ Hamilton cycle chords

Fatima Affif Chaouche, Carrie Rutherford, Robin Whitty

It is known that $\Theta (\log n)$ chords must be added to an $n$-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, $Θ(n…