Dicycle cover of Hamiltonian oriented graphs (Q275871)

Summary: A dicycle cover of a digraph \(D\) is a family \(\mathcal{F}\) of dicycles of \(D\) such that each arc of \(D\) lies in at least one dicycle in \(\mathcal{F}\). We investigate the problem of determining the upper bounds for the minimum number of dicycles which cover all arcs in a strong digraph. Best possible upper bounds of dicycle covers are obtained in a number of classes of digraphs including strong tournaments, Hamiltonian oriented graphs, Hamiltonian oriented complete bipartite graphs, and families of possibly non-Hamiltonian digraphs obtained from these digraphs via a sequence of 2-sum operations.