Abstract
We prove that every graph $G$ has a vertex partition into a cycle and an anticyle (a cycle in the complement of $G$). Emptyset, singletons and edges are considered as cycles. This problem was posed by Lehel and shown to be true for very large graphs by \L uczak, Rödl and Szemerédi~\cite{LRS}, and more recently for large graphs by Allen~\cite{PA}.