The Decomposition of Graphs with Extended Cyclic Triples

Abstract

In this paper, we study the decomposition of the graph $(\lambda D_v{)}^{+\alpha }$ into extended cyclic triples, for all $\lambda \ge \alpha$. By an extended cyclic triple, we mean a loop, a loop with symmetric arcs attached (known as a lollipop), or a directed $3$-cycle (known as a cyclic triple).