Six-cycle systems (Q2054649)

In this paper, the authors survey the existing results on \(6\)-cycle systems. The topics covered are the following: existence of \(6\)-cycle systems with additional properties, enumeration results, embeddings, resolvable and almost resolvable \(6\)-cycle systems, colourings, \(2\)-perfect and almost \(2\)-perfect \(6\)-cycle systems, \(6\)-cycle systems with higher index, metamorphoses, nested \(6\)-cycles systems, intersections, decompositions of bipartite and multipartite graphs in \(6\)-cycle systems, packings and coverings, directed \(6\)-cycles. Moreover, a few enumeration results are included here for the first time. At the end of the paper, the authors give a list of open problems related to \(6\)-cycle systems.