On the Dinitz conjecture and related conjectures Original Research Article

We present previously unpublished elementary proofs by Dekker and Ottens (1991) and Boyce (private communication) of a special case of the Dinitz conjecture. We prove a special case of a related basis conjecture by Rota, and give a reformulation of Rotaʹs conjecture using the Nullstellensatz. Finally we give an asymptotic result on a related Latin square conjecture.