On anti-Novák cycle systems

Abstract

This note is motivated by recent work by Feng et al. (2021) which studies Novák’s conjecture for Steiner Triple Systems and extends it to cyclic Steiner 2-designs, and more generally to cyclic 2-designs. Here we consider instead a generalization to cyclic k-cycle systems: we show that in this setting the generalized conjecture is false for k≥5, and construct some families of counterexamples which arise.