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 -cycle systems: we show that in this setting the generalized conjecture is false for k>4 , and construct some families of counterexamples which arise.
On anti-Novák cycle systems / Buratti, Marco; Merola, Francesca. - In: EXAMPLES AND COUNTEREXAMPLES. - ISSN 2666-657X. - 2:(2022). [10.1016/j.exco.2022.100063]
On anti-Novák cycle systems
Buratti, MarcoMembro del Collaboration Group
;Merola, Francesca
Membro del Collaboration Group
2022
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 -cycle systems: we show that in this setting the generalized conjecture is false for k>4 , and construct some families of counterexamples which arise.File allegati a questo prodotto
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